1
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Storz S, Schär J, Kulikov A, Magnard P, Kurpiers P, Lütolf J, Walter T, Copetudo A, Reuer K, Akin A, Besse JC, Gabureac M, Norris GJ, Rosario A, Martin F, Martinez J, Amaya W, Mitchell MW, Abellan C, Bancal JD, Sangouard N, Royer B, Blais A, Wallraff A. Loophole-free Bell inequality violation with superconducting circuits. Nature 2023; 617:265-270. [PMID: 37165240 PMCID: PMC10172133 DOI: 10.1038/s41586-023-05885-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Accepted: 02/24/2023] [Indexed: 05/12/2023]
Abstract
Superposition, entanglement and non-locality constitute fundamental features of quantum physics. The fact that quantum physics does not follow the principle of local causality1-3 can be experimentally demonstrated in Bell tests4 performed on pairs of spatially separated, entangled quantum systems. Although Bell tests, which are widely regarded as a litmus test of quantum physics, have been explored using a broad range of quantum systems over the past 50 years, only relatively recently have experiments free of so-called loopholes5 succeeded. Such experiments have been performed with spins in nitrogen-vacancy centres6, optical photons7-9 and neutral atoms10. Here we demonstrate a loophole-free violation of Bell's inequality with superconducting circuits, which are a prime contender for realizing quantum computing technology11. To evaluate a Clauser-Horne-Shimony-Holt-type Bell inequality4, we deterministically entangle a pair of qubits12 and perform fast and high-fidelity measurements13 along randomly chosen bases on the qubits connected through a cryogenic link14 spanning a distance of 30 metres. Evaluating more than 1 million experimental trials, we find an average S value of 2.0747 ± 0.0033, violating Bell's inequality with a P value smaller than 10-108. Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with potential applications in quantum communication, quantum computing and fundamental physics15.
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Affiliation(s)
- Simon Storz
- Department of Physics, ETH Zurich, Zurich, Switzerland.
| | - Josua Schär
- Department of Physics, ETH Zurich, Zurich, Switzerland
| | | | - Paul Magnard
- Department of Physics, ETH Zurich, Zurich, Switzerland
- Alice and Bob, Paris, France
| | - Philipp Kurpiers
- Department of Physics, ETH Zurich, Zurich, Switzerland
- Rohde and Schwarz, Munich, Germany
| | - Janis Lütolf
- Department of Physics, ETH Zurich, Zurich, Switzerland
| | - Theo Walter
- Department of Physics, ETH Zurich, Zurich, Switzerland
| | - Adrian Copetudo
- Department of Physics, ETH Zurich, Zurich, Switzerland
- Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore
| | - Kevin Reuer
- Department of Physics, ETH Zurich, Zurich, Switzerland
| | | | | | | | | | | | | | | | | | - Morgan W Mitchell
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain
- ICREA - Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain
| | | | - Jean-Daniel Bancal
- Institute of Theoretical Physics, University of Paris-Saclay, CEA, CNRS, Gif-sur-Yvette, France
| | - Nicolas Sangouard
- Institute of Theoretical Physics, University of Paris-Saclay, CEA, CNRS, Gif-sur-Yvette, France
| | - Baptiste Royer
- Department of Physics, Yale University, New Haven, CT, USA
- Institut quantique and Départment de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada
| | - Alexandre Blais
- Institut quantique and Départment de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario, Canada
| | - Andreas Wallraff
- Department of Physics, ETH Zurich, Zurich, Switzerland.
- Quantum Center, ETH Zurich, Zurich, Switzerland.
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2
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Tong X, He Z, Zhang Y, Solomon S, Lin L, Song Q, Wang LV. Experimental full-domain mapping of quantum correlation in Clauser-Horne-Shimony-Holt scenarios. PHYSICAL REVIEW APPLIED 2023; 19:034049. [PMID: 38249539 PMCID: PMC10798678 DOI: 10.1103/physrevapplied.19.034049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/23/2024]
Abstract
Quantum correlation between two parties serves as an important resource in the surging applications of quantum information. The Bell nonlocality and quantum steering have been proposed to describe non-classical correlations against local-hidden-variable and local-hidden-state theories, respectively. To characterize the two types of non-classical correlations, various nonlocality and steering inequalities have been established, and the amount of inequality violation serves as an important indicator for many entanglement-based tasks. Quantum state tomography has been employed for measuring quantum states, while the method requires intensive computation and does not directly verify either nonlocality or steering over the full domain independent of established theories. Here, we experimentally map the full-domain correlation with bipartite states for nonlocality and quantum steering in CHSH scenarios. The measurement of the maps automatically accounts for detection imperfections. Furthermore, we demonstrate the application of the correlation maps in the entanglement-based quantum key distribution protocol with arbitrary bipartite states. The correlation maps show direct measurements and simple interpretations that can answer fundamental questions about nonlocality and quantum steering as well as contribute to quantum information applications in a straightforward manner.
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Affiliation(s)
| | | | | | - Samuel Solomon
- Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138–78, Pasadena, CA 91125, USA
| | - Li Lin
- Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138–78, Pasadena, CA 91125, USA
| | - Qiyuan Song
- Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138–78, Pasadena, CA 91125, USA
| | - Lihong V. Wang
- Caltech Optical Imaging Laboratory, Andrew and Peggy Cherng Department of Medical Engineering, Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., MC 138–78, Pasadena, CA 91125, USA
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3
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Mandarino A, Scala G. On the Fidelity Robustness of CHSH-Bell Inequality via Filtered Random States. ENTROPY (BASEL, SWITZERLAND) 2023; 25:94. [PMID: 36673235 PMCID: PMC9858419 DOI: 10.3390/e25010094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 12/28/2022] [Accepted: 12/29/2022] [Indexed: 06/17/2023]
Abstract
The theorem developed by John Bell constituted the starting point of a revolution that translated a philosophical question about the nature of reality into the broad and intense field of research of the quantum information technologies. We focus on a system of two qubits prepared in a random, mixed state, and we study the typical behavior of their nonlocality via the CHSH-Bell inequality. Afterward, motivated by the necessity of accounting for inefficiency in the state preparation, we address to what extent states close enough to one with a high degree of nonclassicality can violate local realism with a previously chosen experimental setup.
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4
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Wu D, Jiang YF, Gu XM, Huang L, Bai B, Sun QC, Zhang X, Gong SQ, Mao Y, Zhong HS, Chen MC, Zhang J, Zhang Q, Lu CY, Pan JW. Experimental Refutation of Real-Valued Quantum Mechanics under Strict Locality Conditions. PHYSICAL REVIEW LETTERS 2022; 129:140401. [PMID: 36240393 DOI: 10.1103/physrevlett.129.140401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Revised: 06/29/2022] [Accepted: 08/08/2022] [Indexed: 06/16/2023]
Abstract
Quantum mechanics is commonly formulated in a complex, rather than real, Hilbert space. However, whether quantum theory really needs the participation of complex numbers has been debated ever since its birth. Recently, a Bell-like test in an entanglement-swapping scenario has been proposed to distinguish standard quantum mechanics from its real-valued analog. Previous experiments have conceptually demonstrated, yet not satisfied, the central requirement of independent state preparation and measurements and leave several loopholes. Here, we implement such a Bell-like test with two separated independent sources delivering entangled photons to three separated parties under strict locality conditions that are enforced by spacelike separation of the relevant events, rapid random setting generation, and fast measurement. With the fair-sampling assumption and closed loopholes of independent source, locality, and measurement independence simultaneously, we violate the constraints of real-valued quantum mechanics by 5.30 standard deviations. Our results disprove the real-valued quantum theory to describe nature and ensure the indispensable role of complex numbers in quantum mechanics.
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Affiliation(s)
- Dian Wu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yang-Fan Jiang
- Jinan Institute of Quantum Technology, Jinan 250101, China
| | - Xue-Mei Gu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Liang Huang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Bing Bai
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Qi-Chao Sun
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Xingjian Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Si-Qiu Gong
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yingqiu Mao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Han-Sen Zhong
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Ming-Cheng Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jun Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Qiang Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chao-Yang Lu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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5
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Hu XM, Zhang C, Liu BH, Guo Y, Xing WB, Huang CX, Huang YF, Li CF, Guo GC. High-Dimensional Bell Test without Detection Loophole. PHYSICAL REVIEW LETTERS 2022; 129:060402. [PMID: 36018648 DOI: 10.1103/physrevlett.129.060402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Revised: 04/01/2022] [Accepted: 07/15/2022] [Indexed: 06/15/2023]
Abstract
Violation of Bell's inequalities shows strong conflict between quantum mechanics and local realism. Loophole-free Bell tests not only deepen understanding of quantum mechanics, but are also important foundations for device-independent (DI) tasks in quantum information. High-dimensional quantum systems offer a significant advantage over qubits for closing the detection loophole. In the symmetric scenario, a detection efficiency as low as 61.8% can be tolerated using four-dimensional states and a four-setting Bell inequality [Phys. Rev. Lett. 104, 060401 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.060401]. For the first time, we show that four-dimensional entangled photons violate a Bell inequality while closing the detection loophole in experiment. The detection efficiency of the four-dimensional entangled source is about 71.7%, and the fidelity of the state is 0.995±0.001. Combining the technique of multicore fibers, the realization of loophole-free high-dimensional Bell tests and high-dimensional quantum DI technologies are promising.
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Affiliation(s)
- Xiao-Min Hu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yu Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Wen-Bo Xing
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Cen-Xiao Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yun-Feng Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China and Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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6
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Yi B, Bose S. Quantum Liang Information Flow as Causation Quantifier. PHYSICAL REVIEW LETTERS 2022; 129:020501. [PMID: 35867429 DOI: 10.1103/physrevlett.129.020501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2022] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
Liang information flow is widely used in classical systems and network theory for causality quantification and has been applied widely, for example, to finance, neuroscience, and climate studies. The key part of the theory is to freeze a node of a network to ascertain its causal influence on other nodes. Such a theory is yet to be applied to quantum network dynamics. Here, we generalize the Liang information flow to the quantum domain with respect to von Neumann entropy and exemplify its usage by applying it to a variety of small quantum networks.
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Affiliation(s)
- Bin Yi
- Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom
| | - Sougato Bose
- Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom
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7
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Ham BS. Randomness-based macroscopic Franson-type nonlocal correlation. Sci Rep 2022; 12:3759. [PMID: 35260682 PMCID: PMC8904538 DOI: 10.1038/s41598-022-07740-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 02/14/2022] [Indexed: 11/30/2022] Open
Abstract
Franson-type nonlocal correlation is related to Bell inequality violation tests and has been applied for quantum key distributions based on time bin methods. Using unbalanced Mach–Zehnder interferometers, Franson correlation measurements result in an interference fringe, while local measurements do not. Here, randomness-based macroscopic Franson-type correlation is presented using polarization-based two-mode coherent photons, where the quantum correlation is tested by a Hong-Ou-Mandel scheme. Coherent photons are used to investigate the wave properties of this correlation. Without contradicting the wave-particle duality of quantum mechanics, the proposed method provides fundamental understanding of the quantum nature and opens the door to deterministic quantum information science.
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Affiliation(s)
- Byoung S Ham
- School of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology, 123 Chumdangwagi-ro, Buk-gu, Gwangju, 61005, South Korea.
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8
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Mahdavifar M, Hashemi Rafsanjani SM. Violating Bell inequality using weak coherent states. OPTICS LETTERS 2021; 46:5998-6001. [PMID: 34851943 DOI: 10.1364/ol.441499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 10/31/2021] [Indexed: 06/13/2023]
Abstract
We present an experimental investigation of two-photon interference using a continuous-wave laser. We demonstrate the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality using the phase-randomized weak coherent states from a continuous-wave laser. Our implementation serves as an approach to reveal the quantum nature of a state that is considered to be a classical state.
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9
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The Violation of Bell-CHSH Inequalities Leads to Different Conclusions Depending on the Description Used. ENTROPY 2021; 23:e23070872. [PMID: 34356413 PMCID: PMC8305665 DOI: 10.3390/e23070872] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/19/2021] [Revised: 06/30/2021] [Accepted: 06/30/2021] [Indexed: 11/16/2022]
Abstract
Since the experimental observation of the violation of the Bell-CHSH inequalities, much has been said about the non-local and contextual character of the underlying system. However, the hypothesis from which Bell's inequalities are derived differ according to the probability space used to write them. The violation of Bell's inequalities can, alternatively, be explained by assuming that the hidden variables do not exist at all, that they exist but their values cannot be simultaneously assigned, that the values can be assigned but joint probabilities cannot be properly defined, or that averages taken in different contexts cannot be combined. All of the above are valid options, selected by different communities to provide support to their particular research program.
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10
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Niezgoda A, Chwedeńczuk J. Many-Body Nonlocality as a Resource for Quantum-Enhanced Metrology. PHYSICAL REVIEW LETTERS 2021; 126:210506. [PMID: 34114837 DOI: 10.1103/physrevlett.126.210506] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Accepted: 05/04/2021] [Indexed: 06/12/2023]
Abstract
We demonstrate that the many-body nonlocality witnessed by a broad family of Bell inequalities is a resource for ultraprecise metrology. We formulate a general scheme which allows one to track how the sensitivity grows with the nonlocality extending over an increasing number of particles. We illustrate our findings with some prominent examples-a collection of spins forming an Ising chain and a gas of ultracold atoms in any two-mode configuration. We show that in the vicinity of a quantum critical point the rapid increase of the sensitivity is accompanied by the emergence of the many-body Bell nonlocality. The method described in this work allows for a systematic study of highly quantum phenomena in complex systems, and also extends the understanding of the beneficial role played by fundamental nonclassical effects in implementations of quantum-enhanced protocols.
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Affiliation(s)
- Artur Niezgoda
- Faculty of Physics, University of Warsaw, Ulica Pasteura 5, PL-02-093 Warszawa, Poland
| | - Jan Chwedeńczuk
- Faculty of Physics, University of Warsaw, Ulica Pasteura 5, PL-02-093 Warszawa, Poland
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11
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Wang DZ, Gauthier AQ, Siegmund AE, Hunt KLC. Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers. Phys Chem Chem Phys 2021; 23:6370-6387. [PMID: 33538732 DOI: 10.1039/d0cp05444e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.
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Affiliation(s)
- David Z Wang
- Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA.
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12
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Borselli F, Maiwöger M, Zhang T, Haslinger P, Mukherjee V, Negretti A, Montangero S, Calarco T, Mazets I, Bonneau M, Schmiedmayer J. Two-Particle Interference with Double Twin-Atom Beams. PHYSICAL REVIEW LETTERS 2021; 126:083603. [PMID: 33709745 DOI: 10.1103/physrevlett.126.083603] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2020] [Revised: 12/09/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
We demonstrate a source for correlated pairs of atoms characterized by two opposite momenta and two spatial modes forming a Bell state only involving external degrees of freedom. We characterize the state of the emitted atom beams by observing strong number squeezing up to -10 dB in the correlated two-particle modes of emission. We furthermore demonstrate genuine two-particle interference in the normalized second-order correlation function g^{(2)} relative to the emitted atoms.
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Affiliation(s)
- F Borselli
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
| | - M Maiwöger
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
| | - T Zhang
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
| | - P Haslinger
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
| | - V Mukherjee
- Indian Institute of Science Education and Research, 760010 Berhampur, India
| | - A Negretti
- The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, D-22761 Hamburg, Germany
| | - S Montangero
- Dipartimento di Fisica e Astronomia "G. Galilei," Università di Padova, I-35131 Padova, Italy
- INFN Sezione di Padova, I-35131 Padua, Italy
| | - T Calarco
- Forschungszentrum Jülich, Wilhelm-Johnen-Straße, D-52425 Jülich, Germany and University of Cologne, Institute for Theoretical Physics, D-50937 Cologne, Germany
| | - I Mazets
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
- Research Platform MMM "Mathematics-Magnetism-Materials," c/o Fakultät für Mathematik, Universität Wien, 1090 Vienna, Austria
| | - M Bonneau
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
| | - J Schmiedmayer
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
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13
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Abstract
Chemistry as a natural science occupies the length and temporal scales ranging between the formation of atoms and molecules as quasi-classical objects, and the formation of proto-life systems showing catalytic synthesis, replication, and the capacity for Darwinian evolution. The role of chiral dissymmetry in the chemical evolution toward life is manifested in how the increase of chemical complexity, from atoms and molecules to complex open systems, accompanies the emergence of biological homochirality toward life. Chemistry should express chirality not only as molecular structural dissymmetry that at the present is described in chemical curricula by quite effective pedagogical arguments, but also as a cosmological phenomenon. This relates to a necessarily better understanding of the boundaries of chemistry with physics and biology.
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14
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Bright-light detector control emulates the local bounds of Bell-type inequalities. Sci Rep 2020; 10:13205. [PMID: 32764651 PMCID: PMC7413270 DOI: 10.1038/s41598-020-70045-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2020] [Accepted: 07/15/2020] [Indexed: 11/08/2022] Open
Abstract
It is well-known that no local model-in theory-can simulate the outcome statistics of a Bell-type experiment as long as the detection efficiency is higher than a threshold value. For the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality this theoretical threshold value is [Formula: see text]. On the other hand, Phys. Rev. Lett. 107, 170404 (2011) outlined an explicit practical model that can fake the CHSH inequality for a detection efficiency of up to 0.5. In this work, we close this gap. More specifically, we propose a method to emulate a Bell inequality at the threshold detection efficiency using existing optical detector control techniques. For a Clauser-Horne-Shimony-Holt inequality, it emulates the CHSH violation predicted by quantum mechanics up to [Formula: see text]. For the Garg-Mermin inequality-re-calibrated by incorporating non-detection events-our method emulates its exact local bound at any efficiency above the threshold. This confirms that attacks on secure quantum communication protocols based on Bell violation is a real threat if the detection efficiency loophole is not closed.
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15
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Paneru D, Cohen E, Fickler R, Boyd RW, Karimi E. Entanglement: quantum or classical? REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:064001. [PMID: 32235071 DOI: 10.1088/1361-6633/ab85b9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.
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Affiliation(s)
- Dilip Paneru
- Department of Physics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario, K1N 6N5 Canada
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16
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Quantum Correlations and Quantum Non-Locality: A Review and a Few New Ideas. APPLIED SCIENCES-BASEL 2019. [DOI: 10.3390/app9245406] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject dealing with different but connected facets of quantum non-locality, we consider if this, and the friction it carries with special relativity, can eventually find a “solution” by considering higher dimensional spaces.
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17
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Zhan H, Vanević M, Belzig W. Continuous-Variable Entanglement Test in Driven Quantum Contacts. PHYSICAL REVIEW LETTERS 2019; 122:236801. [PMID: 31298914 DOI: 10.1103/physrevlett.122.236801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2018] [Revised: 03/17/2019] [Indexed: 06/10/2023]
Abstract
The standard entanglement test using the Clauser-Horne-Shimony-Holt inequality is known to fail in mesoscopic junctions at finite temperatures. Since this is due to the bidirectional particle flow, a similar failure is expected to occur in an ac-driven contact. We develop a continuous-variable entanglement test suitable for electrons and holes that are created by the ac drive. At low enough temperatures the generalized Bell inequality is violated in junctions with low conductance or a small number of transport channels and with ac voltages which create few electron-hole pairs per cycle. Our ac-entanglement test depends on the total number of electron-hole pairs and on the distribution of probabilities of pair creations similar to the Fano factor.
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Affiliation(s)
- Hongxin Zhan
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
| | - Mihajlo Vanević
- Department of Physics, University of Belgrade, 11158 Belgrade, Serbia
| | - Wolfgang Belzig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
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18
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Liang YC, Zhang Y. Bounding the Plausibility of Physical Theories in a Device-Independent Setting via Hypothesis Testing. ENTROPY (BASEL, SWITZERLAND) 2019; 21:E185. [PMID: 33266900 PMCID: PMC7514667 DOI: 10.3390/e21020185] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2018] [Revised: 02/12/2019] [Accepted: 02/12/2019] [Indexed: 11/29/2022]
Abstract
The device-independent approach to physics is one where conclusions about physical systems (and hence of Nature) are drawn directly and solely from the observed correlations between measurement outcomes. This operational approach to physics arose as a byproduct of Bell's seminal work to distinguish, via a Bell test, quantum correlations from the set of correlations allowed by local-hidden-variable theories. In practice, since one can only perform a finite number of experimental trials, deciding whether an empirical observation is compatible with some class of physical theories will have to be carried out via the task of hypothesis testing. In this paper, we show that the prediction-based-ratio method-initially developed for performing a hypothesis test of local-hidden-variable theories-can equally well be applied to test many other classes of physical theories, such as those constrained only by the nonsignaling principle, and those that are constrained to produce any of the outer approximation to the quantum set of correlations due to Navascués-Pironio-Acín. We numerically simulate Bell tests using hypothetical nonlocal sources of correlations to illustrate the applicability of the method in both the independent and identically distributed (i.i.d.) scenario and the non-i.i.d. scenario. As a further application, we demonstrate how this method allows us to unveil an apparent violation of the nonsignaling conditions in certain experimental data collected in a Bell test. This, in turn, highlights the importance of the randomization of measurement settings, as well as a consistency check of the nonsignaling conditions in a Bell test.
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Affiliation(s)
- Yeong-Cherng Liang
- Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan
| | - Yanbao Zhang
- NTT Basic Research Laboratories and NTT Research Center for Theoretical Quantum Physics, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
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19
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Efficient Quantum Teleportation of Unknown Qubit Based on DV-CV Interaction Mechanism. ENTROPY 2019; 21:e21020150. [PMID: 33266866 PMCID: PMC7514632 DOI: 10.3390/e21020150] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2018] [Revised: 01/30/2019] [Accepted: 02/01/2019] [Indexed: 12/02/2022]
Abstract
We propose and develop the theory of quantum teleportation of an unknown qubit based on the interaction mechanism between discrete-variable (DV) and continuous-variable (CV) states on highly transmissive beam splitter (HTBS). This DV-CV interaction mechanism is based on the simultaneous displacement of the DV state on equal in absolute value, but opposite in sign displacement amplitudes by coherent components of the hybrid in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary modes. The relative phase of the displaced unknown qubit in the measurement number state basis can vary on opposite, depending on the parity of the basis states in the case of the negative amplitude of displacement that is akin to action of nonlinear effect on the teleported qubit. All measurement outcomes of the quantum teleportation are distinguishable, but the teleported state at Bob’s disposal may acquire a predetermined amplitude-distorting factor. Two methods of getting rid of the factors are considered. The quantum teleportation is considered in various interpretations. A method for increasing the efficiency of quantum teleportation of an unknown qubit is proposed.
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20
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Kent A. Testing causal quantum theory. Proc Math Phys Eng Sci 2019; 474:20180501. [PMID: 30602934 DOI: 10.1098/rspa.2018.0501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Accepted: 11/13/2018] [Indexed: 11/12/2022] Open
Abstract
Causal quantum theory assumes that measurements or collapses are well-defined physical processes, localized in space-time, and never give perfectly reliable outcomes and that the outcome of one measurement only influences the outcomes of others within its future light cone. Although the theory has unusual properties, it is not immediately evident that it is inconsistent with experiment to date. I discuss its implications and experimental tests.
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Affiliation(s)
- Adrian Kent
- Centre for Quantum Information and Foundations, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK.,Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada
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21
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Marinković I, Wallucks A, Riedinger R, Hong S, Aspelmeyer M, Gröblacher S. Optomechanical Bell Test. PHYSICAL REVIEW LETTERS 2018; 121:220404. [PMID: 30547658 DOI: 10.1103/physrevlett.121.220404] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Indexed: 06/09/2023]
Abstract
Over the past few decades, experimental tests of Bell-type inequalities have been at the forefront of understanding quantum mechanics and its implications. These strong bounds on specific measurements on a physical system originate from some of the most fundamental concepts of classical physics-in particular that properties of an object are well-defined independent of measurements (realism) and only affected by local interactions (locality). The violation of these bounds unambiguously shows that the measured system does not behave classically, void of any assumption on the validity of quantum theory. It has also found applications in quantum technologies for certifying the suitability of devices for generating quantum randomness, distributing secret keys and for quantum computing. Here we report on the violation of a Bell inequality involving a massive, macroscopic mechanical system. We create light-matter entanglement between the vibrational motion of two silicon optomechanical oscillators, each comprising approx. 10^{10} atoms, and two optical modes. This state allows us to violate a Bell inequality by more than 4 standard deviations, directly confirming the nonclassical behavior of our optomechanical system under the fair sampling assumption.
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Affiliation(s)
- Igor Marinković
- Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628CJ Delft, Netherlands
| | - Andreas Wallucks
- Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628CJ Delft, Netherlands
| | - Ralf Riedinger
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, A-1090 Vienna, Austria
| | - Sungkun Hong
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, A-1090 Vienna, Austria
| | - Markus Aspelmeyer
- Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, A-1090 Vienna, Austria
| | - Simon Gröblacher
- Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2628CJ Delft, Netherlands
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22
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Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations. ENTROPY 2018; 20:e20110829. [PMID: 33266553 PMCID: PMC7512390 DOI: 10.3390/e20110829] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 08/25/2018] [Revised: 10/05/2018] [Accepted: 10/22/2018] [Indexed: 11/17/2022]
Abstract
We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by 32 and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound 32 for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study.
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23
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Yang C, Xi C, Jing J, He G. Counterpropagating path-entangled photon pair sources based on simultaneous spontaneous parametric down-conversion processes of nonlinear photonic crystal. OPTICS EXPRESS 2018; 26:27945-27954. [PMID: 30469851 DOI: 10.1364/oe.26.027945] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Accepted: 09/20/2018] [Indexed: 06/09/2023]
Abstract
Ultra-bright source of entangled photons is an essential component in optical quantum information processing. Here we propose a counterpropagating path-entangled photon pair sources using a quasi-periodic modulated lithium niobate crystal. The nonlinear crystal designed by a dual-grid method, simultaneously phase-matched two spontaneous parametric down-conversion processes. Signal and idler modes have opposite propagation directions in the two spontaneous parametric down-conversion processes, which is the key to generating path-entangled photon pairs. Compared to copropagating entangled sources, the counterpropagating path-entangled sources result in a much narrower spectrum. The quantum state of the path-entanglement source is not only suited for quantum coding, but also to allow the implementation of complex quantum algorithms on a photonic chip.
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24
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Li MH, Wu C, Zhang Y, Liu WZ, Bai B, Liu Y, Zhang W, Zhao Q, Li H, Wang Z, You L, Munro WJ, Yin J, Zhang J, Peng CZ, Ma X, Zhang Q, Fan J, Pan JW. Test of Local Realism into the Past without Detection and Locality Loopholes. PHYSICAL REVIEW LETTERS 2018; 121:080404. [PMID: 30192594 DOI: 10.1103/physrevlett.121.080404] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2018] [Revised: 06/11/2018] [Indexed: 05/26/2023]
Abstract
Inspired by the recent remarkable progress in the experimental test of local realism, we report here such a test that achieves an efficiency greater than (78%)^{2} for entangled photon pairs separated by 183 m. Further utilizing the randomness in cosmic photons from pairs of stars on the opposite sides of the sky for the measurement setting choices, we not only close the locality and detection loopholes simultaneously, but also test the null hypothesis against local hidden variable mechanisms for events that took place 11 years ago (13 orders of magnitude longer than previous experiments). After considering the bias in measurement setting choices, we obtain an upper bound on the p value of 7.87×10^{-4}, which clearly indicates the rejection with high confidence of potential local hidden variable models. One may further push the time constraint on local hidden variable mechanisms deep into the cosmic history by taking advantage of the randomness in photon emissions from quasars with large aperture telescopes.
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Affiliation(s)
- Ming-Han Li
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Cheng Wu
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Yanbao Zhang
- NTT Basic Research Laboratories and NTT Research Center for Theoretical Quantum Physics, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Wen-Zhao Liu
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Bing Bai
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Yang Liu
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Weijun Zhang
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, People's Republic of China
| | - Qi Zhao
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Hao Li
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, People's Republic of China
| | - Zhen Wang
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, People's Republic of China
| | - Lixing You
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, People's Republic of China
| | - W J Munro
- NTT Basic Research Laboratories and NTT Research Center for Theoretical Quantum Physics, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Juan Yin
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Jun Zhang
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Cheng-Zhi Peng
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Xiongfeng Ma
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Qiang Zhang
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Jingyun Fan
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
| | - Jian-Wei Pan
- Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, People's Republic of China
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25
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Rauch D, Handsteiner J, Hochrainer A, Gallicchio J, Friedman AS, Leung C, Liu B, Bulla L, Ecker S, Steinlechner F, Ursin R, Hu B, Leon D, Benn C, Ghedina A, Cecconi M, Guth AH, Kaiser DI, Scheidl T, Zeilinger A. Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars. PHYSICAL REVIEW LETTERS 2018; 121:080403. [PMID: 30192604 DOI: 10.1103/physrevlett.121.080403] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Revised: 06/14/2018] [Indexed: 06/08/2023]
Abstract
In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago; the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell's inequality by 9.3 standard deviations, corresponding to an estimated p value of ≲7.4×10^{-21}. This experiment pushes back to at least ∼7.8 Gyr ago the most recent time by which any local-realist influences could have exploited the "freedom-of-choice" loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today.
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Affiliation(s)
- Dominik Rauch
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Johannes Handsteiner
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Armin Hochrainer
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Jason Gallicchio
- Department of Physics, Harvey Mudd College, Claremont, California 91711, USA
| | - Andrew S Friedman
- Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla, California 92093, USA
| | - Calvin Leung
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Department of Physics, Harvey Mudd College, Claremont, California 91711, USA
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Bo Liu
- School of Computer, NUDT, 410073 Changsha, China
| | - Lukas Bulla
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Sebastian Ecker
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Fabian Steinlechner
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Rupert Ursin
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Beili Hu
- Department of Physics, Harvey Mudd College, Claremont, California 91711, USA
| | - David Leon
- Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla, California 92093, USA
| | - Chris Benn
- Isaac Newton Group, Apartado 321, 38700 Santa Cruz de La Palma, Spain
| | | | | | - Alan H Guth
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - David I Kaiser
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Thomas Scheidl
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Anton Zeilinger
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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26
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Deng DL. Machine Learning Detection of Bell Nonlocality in Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2018; 120:240402. [PMID: 29957001 DOI: 10.1103/physrevlett.120.240402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Revised: 04/12/2018] [Indexed: 06/08/2023]
Abstract
Machine learning, the core of artificial intelligence and big data science, is one of today's most rapidly growing interdisciplinary fields. Recently, machine learning tools and techniques have been adopted to tackle intricate quantum many-body problems. In this Letter, we introduce machine learning techniques to the detection of quantum nonlocality in many-body systems, with a focus on the restricted-Boltzmann-machine (RBM) architecture. Using reinforcement learning, we demonstrate that RBM is capable of finding the maximum quantum violations of multipartite Bell inequalities with given measurement settings. Our results build a novel bridge between computer-science-based machine learning and quantum many-body nonlocality, which will benefit future studies in both areas.
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Affiliation(s)
- Dong-Ling Deng
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China and Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
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27
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Li T, Zhang X, Zeng Q, Wang B, Zhang X. Experimental simulation of monogamy relation between contextuality and nonlocality in classical light. OPTICS EXPRESS 2018; 26:11959-11975. [PMID: 29716113 DOI: 10.1364/oe.26.011959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2018] [Accepted: 04/14/2018] [Indexed: 06/08/2023]
Abstract
The Clauser-Horne-Shimony-Holt (CHSH) inequality and the Klyachko-Can-Binicioglu-Shumovski (KCBS) inequality present a tradeoff on the no-disturbance (ND) principle. Recently, the fundamental monogamy relation between contextuality and nonlocality in quantum theory has been demonstrated experimentally. Here we show that such a relation and tradeoff can also be simulated in classical optical systems. Using polarization, path and orbital angular momentum of the classical optical beam, in classical optical experiment we have observed the stringent monogamy relation between the two inequalities by implementing the projection measurement. Our results show the application prospect of the concepts developed recently in quantum information science to classical optical system and optical information processing.
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28
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Khrennikov A, Basieva I. Towards Experiments to Test Violation of the Original Bell Inequality. ENTROPY 2018; 20:e20040280. [PMID: 33265371 PMCID: PMC7512796 DOI: 10.3390/e20040280] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Revised: 03/29/2018] [Accepted: 04/11/2018] [Indexed: 11/16/2022]
Abstract
The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser–Horne–Shimony–Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein–Podolsky–Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR–Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound QCHSH=22 to the classical bound CCHSH=2, i.e., FCHSH=QCHSHCCHSH=2 is less than the fraction of the quantum bound for the OB inequality QOB=32 to the classical bound COB=1, i.e., FOB=QOBCOB=32. Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high.
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Affiliation(s)
- Andrei Khrennikov
- International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, 351 95 Växjö, Sweden
- Correspondence:
| | - Irina Basieva
- Prokhorov General Physics Institute, Vavilov str. 38D, 119991 Moscow, Russia
- Department of Psychology, University of London, London WC1E 7HU, UK
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29
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Wasak T, Chwedeńczuk J. Bell Inequality, Einstein-Podolsky-Rosen Steering, and Quantum Metrology with Spinor Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2018; 120:140406. [PMID: 29694142 DOI: 10.1103/physrevlett.120.140406] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Revised: 02/20/2018] [Indexed: 06/08/2023]
Abstract
We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor F=1 Bose-Einstein condensate residing in an optical lattice. We characterize the complete procedure-the local operations, the measurements, and the inequality-necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. Also, the scattered pairs are an excellent many-body resource for the quantum-enhanced metrology. Our results apply to any multimode system where the spin-changing collision drives the scattering into separate regions. The presented inquiry shows that such a system is versatile as it can be used for the tests of nonlocality, quantum metrology, and quantum information.
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Affiliation(s)
- Tomasz Wasak
- Faculty of Physics, University of Warsaw, ulica Pasteura 5, PL-02-093 Warszawa, Poland
| | - Jan Chwedeńczuk
- Faculty of Physics, University of Warsaw, ulica Pasteura 5, PL-02-093 Warszawa, Poland
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30
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Wasak T, Smerzi A, Chwedeńczuk J. Role of Particle Entanglement in the Violation of Bell Inequalities. Sci Rep 2018; 8:1777. [PMID: 29379056 PMCID: PMC5788934 DOI: 10.1038/s41598-018-20034-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Accepted: 01/08/2018] [Indexed: 11/25/2022] Open
Abstract
Entanglement between two separate systems is a necessary resource to violate a Bell inequality in a test of local realism. We demonstrate that to overcome the Bell bound, this correlation must be accompanied by the entanglement between the constituent particles. This happens whenever a super-selection rule prohibits coherences between states with different total number of particles and thus imposes a constraint on feasible local operations in each sub-system. We show that the necessary entanglement between the particles might solely result from their indistinguishability. We also give an example of both mode and particle-entangled pure state, which does not violate any Bell inequality. Our result reveals a fundamental relation between the non-locality and the particle entanglement.
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Affiliation(s)
- Tomasz Wasak
- Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093, Warszawa, Poland
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125, Firenze, Italy
| | - Jan Chwedeńczuk
- Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093, Warszawa, Poland.
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31
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Spooky Action at a Temporal Distance. ENTROPY 2018; 20:e20010041. [PMID: 33265126 PMCID: PMC7512241 DOI: 10.3390/e20010041] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 11/25/2017] [Revised: 01/05/2018] [Accepted: 01/09/2018] [Indexed: 11/16/2022]
Abstract
Since the discovery of Bell’s theorem, the physics community has come to take seriously the possibility that the universe might contain physical processes which are spatially nonlocal, but there has been no such revolution with regard to the possibility of temporally nonlocal processes. In this article, we argue that the assumption of temporal locality is actively limiting progress in the field of quantum foundations. We investigate the origins of the assumption, arguing that it has arisen for historical and pragmatic reasons rather than good scientific ones, then explain why temporal locality is in tension with relativity and review some recent results which cast doubt on its validity.
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32
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Kupczynski M. Can we close the Bohr-Einstein quantum debate? PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2016.0392. [PMID: 28971944 DOI: 10.1098/rsta.2016.0392] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/04/2017] [Indexed: 06/07/2023]
Abstract
Recent experiments allow one to conclude that Bell-type inequalities are indeed violated; thus, it is important to understand what this means and how we can explain the existence of strong correlations between outcomes of distant measurements. Do we have to announce that Einstein was wrong, Nature is non-local and non-local correlations are produced due to quantum magic and emerge, somehow, from outside space-time? Fortunately, such conclusions are unfounded because, if supplementary parameters describing measuring instruments are correctly incorporated in a theoretical model, then Bell-type inequalities may not be proved. We construct a simple probabilistic model allowing these correlations to be explained in a locally causal way. In our model, measurement outcomes are neither predetermined nor produced in an irreducibly random way. We explain why, contrary to the general belief, the introduction of setting-dependent parameters does not restrict experimenters' freedom of choice. Since the violation of Bell-type inequalities does not allow the conclusion that Nature is non-local and that quantum theory is complete, the Bohr-Einstein quantum debate may not be closed. The continuation of this debate is important not only for a better understanding of Nature but also for various practical applications of quantum phenomena.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
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Affiliation(s)
- Marian Kupczynski
- Département de l'Informatique, Université du Québec en Outaouais (UQO), C.P. 1250, succursale Hull, Gatineau, Quebec, Canada J8X 3X 7
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33
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An Approach To “Quantumness” In Coherent Control. ADVANCES IN CHEMICAL PHYSICS 2017. [DOI: 10.1002/9781119324560.ch2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/13/2023]
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34
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Cobley JN, Close GL, Bailey DM, Davison GW. Exercise redox biochemistry: Conceptual, methodological and technical recommendations. Redox Biol 2017; 12:540-548. [PMID: 28371751 PMCID: PMC5377294 DOI: 10.1016/j.redox.2017.03.022] [Citation(s) in RCA: 70] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2017] [Revised: 03/23/2017] [Accepted: 03/24/2017] [Indexed: 12/16/2022] Open
Abstract
Exercise redox biochemistry is of considerable interest owing to its translational value in health and disease. However, unaddressed conceptual, methodological and technical issues complicate attempts to unravel how exercise alters redox homeostasis in health and disease. Conceptual issues relate to misunderstandings that arise when the chemical heterogeneity of redox biology is disregarded: which often complicates attempts to use redox-active compounds and assess redox signalling. Further, that oxidised macromolecule adduct levels reflect formation and repair is seldom considered. Methodological and technical issues relate to the use of out-dated assays and/or inappropriate sample preparation techniques that confound biochemical redox analysis. After considering each of the aforementioned issues, we outline how each issue can be resolved and provide a unifying set of recommendations. We specifically recommend that investigators: consider chemical heterogeneity, use redox-active compounds judiciously, abandon flawed assays, carefully prepare samples and assay buffers, consider repair/metabolism, use multiple biomarkers to assess oxidative damage and redox signalling.
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Affiliation(s)
- James N Cobley
- Department for Sport and Exercise Sciences, Abertay University, 40 Bell Street, Dundee, Scotland DD1 1HG, UK.
| | - Graeme L Close
- Research Institute for Sport and Exercise Sciences, Liverpool John Moores University, Tom Reilly Building, Liverpool, England L3 3AF, UK
| | - Damian M Bailey
- Neurovascular Research Laboratory, Faculty of Life Sciences and Education, University of South Wales, Wales, CF37 4AT, UK; Faculty of Medicine, Reichwald Health Sciences Centre, University of British Columbia-Okanagan, Kelowna, British Columbia, Canada
| | - Gareth W Davison
- Sport and Exercise Science Research Institute, Ulster University, Belfast, BT37 OQB, UK
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35
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Bai XM, Gao CP, Li JQ, Liu N, Liang JQ. Entanglement dynamics for two spins in an optical cavity - field interaction induced decoherence and coherence revival. OPTICS EXPRESS 2017; 25:17051-17065. [PMID: 28789202 DOI: 10.1364/oe.25.017051] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Accepted: 07/01/2017] [Indexed: 06/07/2023]
Abstract
We in this paper study quantum correlations for two neutral spin-particles coupled with a single-mode optical cavity through the usual magnetic interaction. Two-spin entangled states for both antiparallel and parallel spin-polarizations are generated under the photon coherent-state assumption. Based on the quantum master equation we derive the time-dependent quantum correlation of Clauser-Horne-Shimony-Holt (CHSH) type explicitly in comparison with the well known entanglement-measure concurrence. In the two-spin singlet state, which is recognized as one eigenstate of the system, the CHSH correlation and concurrence remain in their maximum values invariant with time and independent of the average photon-numbers either. The correlation varies periodically with time in the general entangled-states for the low average photon-numbers. When the photon number increases to a certain value the oscillation becomes random and the correlations are suppressed below the Bell bound indicating the decoherence of the entangled states. In the high photon-number limit the coherence revivals periodically such that the CHSH correlation approaches the upper bound value at particular time points associated with the cavity-field period.
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36
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Rosenfeld W, Burchardt D, Garthoff R, Redeker K, Ortegel N, Rau M, Weinfurter H. Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes. PHYSICAL REVIEW LETTERS 2017; 119:010402. [PMID: 28731745 DOI: 10.1103/physrevlett.119.010402] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2016] [Indexed: 05/26/2023]
Abstract
An experimental test of Bell's inequality allows ruling out any local-realistic description of nature by measuring correlations between distant systems. While such tests are conceptually simple, there are strict requirements concerning the detection efficiency of the involved measurements, as well as the enforcement of spacelike separation between the measurement events. Only very recently could both loopholes be closed simultaneously. Here we present a statistically significant, event-ready Bell test based on combining heralded entanglement of atoms separated by 398 m with fast and efficient measurements of the atomic spin states closing essential loopholes. We obtain a violation with S=2.221±0.033 (compared to the maximal value of 2 achievable with models based on local hidden variables) which allows us to refute the hypothesis of local realism with a significance level P<2.57×10^{-9}.
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Affiliation(s)
- Wenjamin Rosenfeld
- Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80799 München, Germany
- Max-Planck Institut für Quantenoptik, D-85748 Garching, Germany
| | - Daniel Burchardt
- Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80799 München, Germany
| | - Robert Garthoff
- Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80799 München, Germany
| | - Kai Redeker
- Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80799 München, Germany
| | - Norbert Ortegel
- Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80799 München, Germany
| | - Markus Rau
- Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80799 München, Germany
| | - Harald Weinfurter
- Fakultät für Physik, Ludwig-Maximilians-Universität München, D-80799 München, Germany
- Max-Planck Institut für Quantenoptik, D-85748 Garching, Germany
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37
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Stockill R, Stanley MJ, Huthmacher L, Clarke E, Hugues M, Miller AJ, Matthiesen C, Le Gall C, Atatüre M. Phase-Tuned Entangled State Generation between Distant Spin Qubits. PHYSICAL REVIEW LETTERS 2017; 119:010503. [PMID: 28731764 DOI: 10.1103/physrevlett.119.010503] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2017] [Indexed: 05/13/2023]
Abstract
Quantum entanglement between distant qubits is an important feature of quantum networks. Distribution of entanglement over long distances can be enabled through coherently interfacing qubit pairs via photonic channels. Here, we report the realization of optically generated quantum entanglement between electron spin qubits confined in two distant semiconductor quantum dots. The protocol relies on spin-photon entanglement in the trionic Λ system and quantum erasure of the Raman-photon path information. The measurement of a single Raman photon is used to project the spin qubits into a joint quantum state with an interferometrically stabilized and tunable relative phase. We report an average Bell-state fidelity for |ψ^{(+)}⟩ and |ψ^{(-)}⟩ states of 61.6±2.3% and a record-high entanglement generation rate of 7.3 kHz between distant qubits.
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Affiliation(s)
- R Stockill
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - M J Stanley
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - L Huthmacher
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - E Clarke
- EPSRC National Centre for III-V Technologies, University of Sheffield, Sheffield S1 3JD, United Kingdom
| | - M Hugues
- Université Côte d'Azur, CNRS, CRHEA, rue Bernard Grégory, Valbonne 06560, France
| | - A J Miller
- Quantum Opus, LLC, 45211 Helm St., Plymouth, Michigan 48170, USA
| | - C Matthiesen
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - C Le Gall
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - M Atatüre
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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38
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Tan TR, Wan Y, Erickson S, Bierhorst P, Kienzler D, Glancy S, Knill E, Leibfried D, Wineland DJ. Chained Bell Inequality Experiment with High-Efficiency Measurements. PHYSICAL REVIEW LETTERS 2017; 118:130403. [PMID: 28409945 DOI: 10.1103/physrevlett.118.130403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2016] [Indexed: 06/07/2023]
Abstract
We report correlation measurements on two ^{9}Be^{+} ions that violate a chained Bell inequality obeyed by any local-realistic theory. The correlations can be modeled as derived from a mixture of a local-realistic probabilistic distribution and a distribution that violates the inequality. A statistical framework is formulated to quantify the local-realistic fraction allowable in the observed distribution without the fair-sampling or independent-and-identical-distributions assumptions. We exclude models of our experiment whose local-realistic fraction is above 0.327 at the 95% confidence level. This bound is significantly lower than 0.586, the minimum fraction derived from a perfect Clauser-Horne-Shimony-Holt inequality experiment. Furthermore, our data provide a device-independent certification of the deterministically created Bell states.
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Affiliation(s)
- T R Tan
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Y Wan
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - S Erickson
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - P Bierhorst
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - D Kienzler
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - S Glancy
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - E Knill
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - D Leibfried
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - D J Wineland
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
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39
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Abstract
The concept of randomness plays an important part in many disciplines. On the one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other, randomness is a resource for cryptography, algorithms and simulations. Standard methods for generating randomness rely on assumptions about the devices that are often not valid in practice. However, quantum technologies enable new methods for generating certified randomness, based on the violation of Bell inequalities. These methods are referred to as device-independent because they do not rely on any modelling of the devices. Here we review efforts to design device-independent randomness generators and the associated challenges.
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40
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Handsteiner J, Friedman AS, Rauch D, Gallicchio J, Liu B, Hosp H, Kofler J, Bricher D, Fink M, Leung C, Mark A, Nguyen HT, Sanders I, Steinlechner F, Ursin R, Wengerowsky S, Guth AH, Kaiser DI, Scheidl T, Zeilinger A. Cosmic Bell Test: Measurement Settings from Milky Way Stars. PHYSICAL REVIEW LETTERS 2017; 118:060401. [PMID: 28234500 DOI: 10.1103/physrevlett.118.060401] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2016] [Indexed: 06/06/2023]
Abstract
Bell's theorem states that some predictions of quantum mechanics cannot be reproduced by a local-realist theory. That conflict is expressed by Bell's inequality, which is usually derived under the assumption that there are no statistical correlations between the choices of measurement settings and anything else that can causally affect the measurement outcomes. In previous experiments, this "freedom of choice" was addressed by ensuring that selection of measurement settings via conventional "quantum random number generators" was spacelike separated from the entangled particle creation. This, however, left open the possibility that an unknown cause affected both the setting choices and measurement outcomes as recently as mere microseconds before each experimental trial. Here we report on a new experimental test of Bell's inequality that, for the first time, uses distant astronomical sources as "cosmic setting generators." In our tests with polarization-entangled photons, measurement settings were chosen using real-time observations of Milky Way stars while simultaneously ensuring locality. Assuming fair sampling for all detected photons, and that each stellar photon's color was set at emission, we observe statistically significant ≳7.31σ and ≳11.93σ violations of Bell's inequality with estimated p values of ≲1.8×10^{-13} and ≲4.0×10^{-33}, respectively, thereby pushing back by ∼600 years the most recent time by which any local-realist influences could have engineered the observed Bell violation.
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Affiliation(s)
- Johannes Handsteiner
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Andrew S Friedman
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Dominik Rauch
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Jason Gallicchio
- Department of Physics, Harvey Mudd College, Claremont, California 91711, USA
| | - Bo Liu
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- School of Computer, NUDT, 410073 Changsha, China
| | - Hannes Hosp
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Johannes Kofler
- Max Planck Institute of Quantum Optics, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - David Bricher
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Matthias Fink
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Calvin Leung
- Department of Physics, Harvey Mudd College, Claremont, California 91711, USA
| | - Anthony Mark
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Hien T Nguyen
- NASA Jet Propulsion Laboratory, Pasadena, California 91109, USA
| | - Isabella Sanders
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Fabian Steinlechner
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Rupert Ursin
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Sören Wengerowsky
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Alan H Guth
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - David I Kaiser
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Thomas Scheidl
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Anton Zeilinger
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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41
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Ciborowski J, Caban P, Drągowski M, Enders J, Fritzsche Y, Poliszczuk A, Rembieliński J, Włodarczyk M. A project to measure quantum spin correlations of relativistic electron pairs in Møller scattering. EPJ WEB OF CONFERENCES 2017. [DOI: 10.1051/epjconf/201716401004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Zhang C, Zhang CJ, Huang YF, Hou ZB, Liu BH, Li CF, Guo GC. Experimental test of genuine multipartite nonlocality under the no-signalling principle. Sci Rep 2016; 6:39327. [PMID: 27996055 PMCID: PMC5171240 DOI: 10.1038/srep39327] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2016] [Accepted: 11/22/2016] [Indexed: 11/21/2022] Open
Abstract
Genuine multipartite nonlocality (GMN) has been recognized as the strongest form of multipartite quantum correlation. However, there exist states that cannot violate the Svetlichny inequality derived from the standard definition of GMN, even though they possess GMN properties. The reason is that the standard definition of GMN allows correlations that permit signalling among parties, which is inconsistent with an operational definition. Here, for the first time, we present an experimental test of GMN in the no-signalling scenario, with a three-photon pure state |ψs〉 and a noisy W state. The experimental results show that these states cannot violate the Svetlichny inequality. However, our results also demonstrate that they do violate a new inequality derived from the definition of GMN based on the no-signalling principle, i.e., these states can exhibit GMN under the requirement of no-signalling. Our results will be useful for the study and applications of GMN in quantum communications and quantum computation.
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Affiliation(s)
- Chao Zhang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, P.R. China
| | - Cheng-Jie Zhang
- College of Physics, Optoelectronics and Energy, Soochow University, Suzhou, 215006, China
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Yun-Feng Huang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, P.R. China
| | - Zhi-Bo Hou
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, P.R. China
| | - Bi-Heng Liu
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, P.R. China
| | - Chuan-Feng Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, P.R. China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, P.R. China
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43
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Abstract
Einstein was wrong with his 1927 Solvay Conference claim that quantum mechanics is incomplete and incapable of describing diffraction of single particles. However, the Einstein-Podolsky-Rosen paradox of entangled pairs of particles remains lurking with its 'spooky action at a distance'. In molecules quantum entanglement can be viewed as basis of both chemical bonding and excitonic states. The latter are important in many biophysical contexts and involve coupling between subsystems in which virtual excitations lead to eigenstates of the total Hamiltonian, but not for the separate subsystems. The author questions whether atomic or photonic systems may be probed to prove that particles or photons may stay entangled over large distances and display the immediate communication with each other that so concerned Einstein. A dissociating hydrogen molecule is taken as a model of a zero-spin entangled system whose angular momenta are in principle possible to probe for this purpose. In practice, however, spins randomize as a result of interactions with surrounding fields and matter. Similarly, no experiment seems yet to provide unambiguous evidence of remaining entanglement between single photons at large separations in absence of mutual interaction, or about immediate (superluminal) communication. This forces us to reflect again on what Einstein really had in mind with the paradox, viz. a probabilistic interpretation of a wave function for an ensemble of identically prepared states, rather than as a statement about single particles. Such a prepared state of many particles would lack properties of quantum entanglement that make it so special, including the uncertainty upon which safe quantum communication is assumed to rest. An example is Zewail's experiment showing visible resonance in the dissociation of a coherently vibrating ensemble of NaI molecules apparently violating the uncertainty principle. Einstein was wrong about diffracting single photons where space-like anti-bunching observations have proven recently their non-local character and how observation in one point can remotely affect the outcome in other points. By contrast, long range photon entanglement with immediate, superluminal response is still an elusive, possibly partly misunderstood issue. The author proposes that photons may entangle over large distances only if some interaction exists via fields that cannot propagate faster than the speed of light. An experiment to settle this 'interaction hypothesis' is suggested.
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Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis. Sci Rep 2016; 6:30289. [PMID: 27509823 PMCID: PMC4980695 DOI: 10.1038/srep30289] [Citation(s) in RCA: 52] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Accepted: 06/27/2016] [Indexed: 11/29/2022] Open
Abstract
The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682–686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, in agreement with the first run, yielding an overall value of S = 2.38 ± 0.14. We calculate the resulting P-values of the second experiment and of the combined Bell tests. We provide an additional analysis of the distribution of settings choices recorded during the two tests, finding that the observed distributions are consistent with uniform settings for both tests. Finally, we analytically study the effect of particular models of random number generator (RNG) imperfection on our hypothesis test. We find that the winning probability per trial in the CHSH game can be bounded knowing only the mean of the RNG bias. This implies that our experimental result is robust for any model underlying the estimated average RNG bias, for random bits produced up to 690 ns too early by the random number generator.
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Chen SL, Budroni C, Liang YC, Chen YN. Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing. PHYSICAL REVIEW LETTERS 2016; 116:240401. [PMID: 27367365 DOI: 10.1103/physrevlett.116.240401] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2016] [Indexed: 06/06/2023]
Abstract
We introduce the concept of assemblage moment matrices, i.e., a collection of matrices of expectation values, each associated with a conditional quantum state obtained in a steering experiment. We demonstrate how it can be used for quantum states and measurements characterization in a device-independent manner, i.e., without invoking any assumption about the measurement or the preparation device. Specifically, we show how the method can be used to lower bound the steerability of an underlying quantum state directly from the observed correlation between measurement outcomes. Combining such device-independent quantifications with earlier results established by Piani and Watrous [Phys. Rev. Lett. 114, 060404 (2015)], our approach immediately provides a device-independent lower bound on the generalized robustness of entanglement, as well as the usefulness of the underlying quantum state for a type of subchannel discrimination problem. In addition, by proving a quantitative relationship between steering robustness and the recently introduced incompatibility robustness, our approach also allows for a device-independent quantification of the incompatibility between various measurements performed in a Bell-type experiment. Explicit examples where such bounds provide a kind of self-testing of the performed measurements are provided.
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Affiliation(s)
- Shin-Liang Chen
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Costantino Budroni
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany
| | - Yeong-Cherng Liang
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Yueh-Nan Chen
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
- Physics Division, National Center for Theoretical Sciences, Hsinchu 300, Taiwan
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47
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Coppersmith S. Quantum information: Violation of Bell's inequality in Si. NATURE NANOTECHNOLOGY 2016; 11:216-217. [PMID: 26936815 DOI: 10.1038/nnano.2016.26] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Affiliation(s)
- Susan Coppersmith
- Department of Physics, University of Wisconsin, Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA
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Dehollain JP, Simmons S, Muhonen JT, Kalra R, Laucht A, Hudson F, Itoh KM, Jamieson DN, McCallum JC, Dzurak AS, Morello A. Bell's inequality violation with spins in silicon. NATURE NANOTECHNOLOGY 2016; 11:242-246. [PMID: 26571006 DOI: 10.1038/nnano.2015.262] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2015] [Accepted: 10/07/2015] [Indexed: 06/05/2023]
Abstract
Bell's theorem proves the existence of entangled quantum states with no classical counterpart. An experimental violation of Bell's inequality demands simultaneously high fidelities in the preparation, manipulation and measurement of multipartite quantum entangled states, and provides a single-number benchmark for the performance of devices that use such states for quantum computing. We demonstrate a Bell/ Clauser-Horne-Shimony-Holt inequality violation with Bell signals up to 2.70(9), using the electron and the nuclear spins of a single phosphorus atom embedded in a silicon nanoelectronic device. Two-qubit state tomography reveals that our prepared states match the target maximally entangled Bell states with >96% fidelity. These experiments demonstrate complete control of the two-qubit Hilbert space of a phosphorus atom and highlight the important function of the nuclear qubit to expand the computational basis and maximize the readout fidelity.
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Affiliation(s)
- Juan P Dehollain
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Stephanie Simmons
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Juha T Muhonen
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Rachpon Kalra
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Arne Laucht
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Fay Hudson
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Kohei M Itoh
- School of Fundamental Science and Technology, Keio University, 3-14-1 Hiyoshi, 223-8522, Japan
| | - David N Jamieson
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Jeffrey C McCallum
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Andrew S Dzurak
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
| | - Andrea Morello
- Centre for Quantum Computation and Communication Technology, UNSW Australia, Sydney, New South Wales 2052, Australia
- School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia
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Ballance CJ, Schäfer VM, Home JP, Szwer DJ, Webster SC, Allcock DTC, Linke NM, Harty TP, Aude Craik DPL, Stacey DN, Steane AM, Lucas DM. Hybrid quantum logic and a test of Bell's inequality using two different atomic isotopes. Nature 2016; 528:384-6. [PMID: 26672554 DOI: 10.1038/nature16184] [Citation(s) in RCA: 71] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2015] [Accepted: 10/26/2015] [Indexed: 11/09/2022]
Abstract
Entanglement is one of the most fundamental properties of quantum mechanics, and is the key resource for quantum information processing (QIP). Bipartite entangled states of identical particles have been generated and studied in several experiments, and post-selected or heralded entangled states involving pairs of photons, single photons and single atoms, or different nuclei in the solid state, have also been produced. Here we use a deterministic quantum logic gate to generate a 'hybrid' entangled state of two trapped-ion qubits held in different isotopes of calcium, perform full tomography of the state produced, and make a test of Bell's inequality with non-identical atoms. We use a laser-driven two-qubit gate, whose mechanism is insensitive to the qubits' energy splittings, to produce a maximally entangled state of one (40)Ca(+) qubit and one (43)Ca(+) qubit, held 3.5 micrometres apart in the same ion trap, with 99.8 ± 0.6 per cent fidelity. We test the CHSH (Clauser-Horne-Shimony-Holt) version of Bell's inequality for this novel entangled state and find that it is violated by 15 standard deviations; in this test, we close the detection loophole but not the locality loophole. Mixed-species quantum logic is a powerful technique for the construction of a quantum computer based on trapped ions, as it allows protection of memory qubits while other qubits undergo logic operations or are used as photonic interfaces to other processing units. The entangling gate mechanism used here can also be applied to qubits stored in different atomic elements; this would allow both memory and logic gate errors caused by photon scattering to be reduced below the levels required for fault-tolerant quantum error correction, which is an essential prerequisite for general-purpose quantum computing.
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Affiliation(s)
- C J Ballance
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - V M Schäfer
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - J P Home
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D J Szwer
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - S C Webster
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D T C Allcock
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - N M Linke
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - T P Harty
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D P L Aude Craik
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D N Stacey
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - A M Steane
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
| | - D M Lucas
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
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50
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Zhang C, Huang YF, Wang Z, Liu BH, Li CF, Guo GC. Experimental Greenberger-Horne-Zeilinger-Type Six-Photon Quantum Nonlocality. PHYSICAL REVIEW LETTERS 2015; 115:260402. [PMID: 26764975 DOI: 10.1103/physrevlett.115.260402] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2015] [Indexed: 06/05/2023]
Abstract
Quantum nonlocality gives us deeper insight into quantum physics. In addition, quantum nonlocality has been further recognized as an essential resource for device-independent quantum information processing in recent years. Most experiments of nonlocality are performed using a photonic system. However, until now, photonic experiments of nonlocality have involved at most four photons. Here, for the first time, we experimentally demonstrate the six-photon quantum nonlocality in an all-versus-nothing manner based on a high-fidelity (88.4%) six-photon Greenberger-Horne-Zeilinger state. Our experiment pushes multiphoton nonlocality studies forward to the six-photon region and might provide a larger photonic system for device-independent quantum information protocols.
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Affiliation(s)
- Chao Zhang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Yun-Feng Huang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zhao Wang
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Bi-Heng Liu
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, People's Republic of China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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