1
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Xu ZP, Saha D, Bharti K, Cabello A. Certifying Sets of Quantum Observables with Any Full-Rank State. PHYSICAL REVIEW LETTERS 2024; 132:140201. [PMID: 38640382 DOI: 10.1103/physrevlett.132.140201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 02/10/2024] [Accepted: 03/01/2024] [Indexed: 04/21/2024]
Abstract
We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets by looking at the statistics of experiments with sequential measurements and using any initial state of full rank, including thermal and maximally mixed states. We prove that this "certification with any full-rank state" (CFR) is possible for any quantum system of finite dimension d≥3 and is robust and experimentally useful in dimensions 3 and 4. In addition, we prove that complete Kochen-Specker sets can be Bell self-tested if and only if they enable CFR. This establishes a fundamental connection between these two methods of certification, shows that both methods can be combined in the same experiment, and opens new possibilities for certifying quantum devices.
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Affiliation(s)
- Zhen-Peng Xu
- School of Physics and Optoelectronics Engineering, Anhui University, 230601 Hefei, People's Republic of China
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Debashis Saha
- School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala 695551, India
| | - Kishor Bharti
- Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Republic of Singapore
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
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2
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Fan X, Xiao Y, Gu Y. Demonstration of universal contextuality through communication games free of both operational inequivalence and compatibility loopholes. OPTICS EXPRESS 2023; 31:42764-42784. [PMID: 38178388 DOI: 10.1364/oe.502723] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 11/18/2023] [Indexed: 01/06/2024]
Abstract
Universal contextuality is the leading notion of non-classicality even for single systems, showing its advantage as a more general quantum correlation than Bell non-locality, as well as preparation contextuality. However, a loophole-free experimental demonstration of universal contextuality at least requires that both operational inequivalence and compatibility loopholes are closed, which have never been simultaneously achieved to date. In our work, we experimentally test universal contextuality through (3,3) and (4,3) communication games, simultaneously restoring operational equivalence and circumventing the compatibility loophole. Our result exhibits the violation of universal non-contextuality bound by 97 standard deviations in (3,3) scenario, and 107 deviations in (4,3) scenario. Notably there are states which exhibit locality but reveal universal contextuality in both two scenarios. In addition, our result shows that universal contextuality is more general than preparation contextuality in (3,3) scenario, while equivalent to preparation contextuality in (4,3) scenario.
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3
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Liu ZH, Meng HX, Xu ZP, Zhou J, Chen JL, Xu JS, Li CF, Guo GC, Cabello A. Experimental Test of High-Dimensional Quantum Contextuality Based on Contextuality Concentration. PHYSICAL REVIEW LETTERS 2023; 130:240202. [PMID: 37390410 DOI: 10.1103/physrevlett.130.240202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Accepted: 05/09/2023] [Indexed: 07/02/2023]
Abstract
Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here, we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality "concentrates" as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.
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Affiliation(s)
- Zheng-Hao Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Centre For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Hui-Xian Meng
- School of Mathematics and Physics, North China Electric Power University, Beijing 102206, People's Republic of China
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
| | - Zhen-Peng Xu
- School of Physics and Optoelectronics Engineering, Anhui University, 230601 Hefei, People's Republic of China
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Jie Zhou
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
- Centre for Quantum Technologies, National University of Singapore, 117543, Singapore
| | - Jing-Ling Chen
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Centre For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Centre For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Centre For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, People's Republic of China
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
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4
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Hrmo P, Wilhelm B, Gerster L, van Mourik MW, Huber M, Blatt R, Schindler P, Monz T, Ringbauer M. Native qudit entanglement in a trapped ion quantum processor. Nat Commun 2023; 14:2242. [PMID: 37076475 PMCID: PMC10115791 DOI: 10.1038/s41467-023-37375-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2023] [Accepted: 03/15/2023] [Indexed: 04/21/2023] Open
Abstract
Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate up to dimension 5 in a trapped-ion system. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.
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Affiliation(s)
- Pavel Hrmo
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria.
| | - Benjamin Wilhelm
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Lukas Gerster
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Martin W van Mourik
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Marcus Huber
- Atominstitut, Technische Universität Wien, 1020, Vienna, Austria
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090, Vienna, Austria
| | - Rainer Blatt
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21a, 6020, Innsbruck, Austria
- AQT, Technikerstraße 17, 6020, Innsbruck, Austria
| | - Philipp Schindler
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Thomas Monz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
- AQT, Technikerstraße 17, 6020, Innsbruck, Austria
| | - Martin Ringbauer
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
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5
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Booth RI, Chabaud U, Emeriau PE. Contextuality and Wigner Negativity Are Equivalent for Continuous-Variable Quantum Measurements. PHYSICAL REVIEW LETTERS 2022; 129:230401. [PMID: 36563212 DOI: 10.1103/physrevlett.129.230401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 10/24/2022] [Indexed: 06/17/2023]
Abstract
Quantum computers promise considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting-a promising paradigm for the realization of universal, scalable, and fault-tolerant quantum computing-contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way toward practical demonstrations of continuous-variable contextuality and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.
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Affiliation(s)
- Robert I Booth
- School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, United Kingdom
- LORIA CNRS, Inria-MOCQUA, Université de Lorraine, F-54000 Nancy, France
- Sorbonne Université, CNRS, LIP6, F-75005 Paris, France
| | - Ulysse Chabaud
- Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
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6
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Wang P, Zhang J, Luan CY, Um M, Wang Y, Qiao M, Xie T, Zhang JN, Cabello A, Kim K. Significant loophole-free test of Kochen-Specker contextuality using two species of atomic ions. SCIENCE ADVANCES 2022; 8:eabk1660. [PMID: 35138888 PMCID: PMC8827658 DOI: 10.1126/sciadv.abk1660] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 12/16/2021] [Indexed: 05/28/2023]
Abstract
Quantum measurements cannot be thought of as revealing preexisting results, even when they do not disturb any other measurement in the same trial. This feature is called contextuality and is crucial for the quantum advantage in computing. Here, we report the observation of quantum contextuality simultaneously free of the detection, sharpness, and compatibility loopholes. The detection and sharpness loopholes are closed by adopting a hybrid two-ion system and highly efficient fluorescence measurements offering a detection efficiency of 100% and a measurement repeatability of >98%. The compatibility loophole is closed by targeting correlations between observables for two different ions in a Paul trap, a 171Yb+ ion and a 138Ba+ ion, chosen so measurements on each ion use different operation laser wavelengths, fluorescence wavelengths, and detectors. The experimental results show a violation of the bound for the most adversarial noncontextual models and open a way to certify quantum systems.
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Affiliation(s)
- Pengfei Wang
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People’s Republic of China
| | - Junhua Zhang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, People’s Republic of China
| | - Chun-Yang Luan
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Mark Um
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Ye Wang
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA
| | - Mu Qiao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
| | - Tian Xie
- Kavli Nanoscience Institute and Thomas J. Watson Sr., Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Jing-Ning Zhang
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People’s Republic of China
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Kihwan Kim
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, People’s Republic of China
- Frontier Science Center for Quantum Information, Beijing 100084, People’s Republic of China
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7
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Cabello A. Converting Contextuality into Nonlocality. PHYSICAL REVIEW LETTERS 2021; 127:070401. [PMID: 34459651 DOI: 10.1103/physrevlett.127.070401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Revised: 04/20/2021] [Accepted: 07/07/2021] [Indexed: 06/13/2023]
Abstract
We introduce a general method which converts, in a unified way, any form of quantum contextuality, including any form of state-dependent contextuality, into a quantum violation of a bipartite Bell inequality. As an example, we apply the method to a quantum violation of the Klyachko-Can-Binicioğlu-Shumovsky inequality.
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Affiliation(s)
- Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
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8
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Xu ZP, Chen JL, Gühne O. Proof of the Peres Conjecture for Contextuality. PHYSICAL REVIEW LETTERS 2020; 124:230401. [PMID: 32603161 DOI: 10.1103/physrevlett.124.230401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2020] [Revised: 04/24/2020] [Accepted: 05/15/2020] [Indexed: 06/11/2023]
Abstract
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics cannot be reconciled with classical models that are noncontextual for ideal measurements. The first explicit derivation by Kochen and Specker was rather complex, but considerable simplifications have been achieved thereafter. We propose a systematic approach to find minimal Hardy-type and Greenberger-Horne-Zeilinger-type (GHZ-type) proofs of the Kochen-Specker theorem, these are characterized by the fact that the predictions of classical models are opposite to the predictions of quantum mechanics. Based on our results, we show that the Kochen-Specker set with 18 vectors from Cabello et al. [Phys. Lett. A 212, 183 (1996)PYLAAG0375-960110.1016/0375-9601(96)00134-X] is the minimal set for any dimension, verifying a longstanding conjecture by Peres. Our results allow to identify minimal contextuality scenarios and to study their usefulness for information processing.
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Affiliation(s)
- Zhen-Peng Xu
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
| | - Jing-Ling Chen
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
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9
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Abstract
State-independent contextuality is a fundamental phenomenon in quantum mechanics, which has been demonstrated experimentally in different systems in recent years. Here we show that such contextuality can also be simulated in classical optical systems. Using path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), here the term ‘cetrit’ is the classical counterpart of a qutrit in quantum systems. Furthermore, in classical optical systems we have simulated the violations of several Yu-Oh-like noncontextual inequalities in a state-independent manner by implementing the projection measurements. Our results not only provide new physical insights into the contextuality and also show the application prospects of the concepts developed recently in quantum information science to classical optical systems and optical information processes.
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10
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van Dam SB, Cramer J, Taminiau TH, Hanson R. Multipartite Entanglement Generation and Contextuality Tests Using Nondestructive Three-Qubit Parity Measurements. PHYSICAL REVIEW LETTERS 2019; 123:050401. [PMID: 31491297 DOI: 10.1103/physrevlett.123.050401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2019] [Indexed: 06/10/2023]
Abstract
We report on the realization and application of nondestructive three-qubit parity measurements on nuclear spin qubits in diamond. We use high-fidelity quantum logic to map the parity of the joint state of three nuclear spin qubits onto an electronic spin qubit that acts as an ancilla, followed by a single-shot nondestructive readout of the ancilla combined with an electron spin echo to ensure outcome-independent evolution of the nuclear spins. Through the sequential application of three such parity measurements, we demonstrate the generation of genuine multipartite entangled states out of the maximally mixed state. Furthermore, we implement a single-shot version of the Greenberger-Horne-Zeilinger experiment that can generate a quantum versus classical contradiction in each run. Finally, we test a state-independent noncontextuality inequality in eight dimensions. The techniques and insights developed are relevant for fundamental tests as well as for quantum information protocols such as quantum error correction.
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Affiliation(s)
- S B van Dam
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands and Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
| | - J Cramer
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands and Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
| | - T H Taminiau
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands and Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
| | - R Hanson
- QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands and Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
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11
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Leupold FM, Malinowski M, Zhang C, Negnevitsky V, Cabello A, Alonso J, Home JP. Sustained State-Independent Quantum Contextual Correlations from a Single Ion. PHYSICAL REVIEW LETTERS 2018; 120:180401. [PMID: 29775358 DOI: 10.1103/physrevlett.120.180401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2017] [Revised: 03/15/2018] [Indexed: 05/02/2023]
Abstract
We use a single trapped-ion qutrit to demonstrate the quantum-state-independent violation of noncontextuality inequalities using a sequence of randomly chosen quantum nondemolition projective measurements. We concatenate 53×10^{6} sequential measurements of 13 observables, and unambiguously violate an optimal noncontextual bound. We use the same data set to characterize imperfections including signaling and repeatability of the measurements. The experimental sequence was generated in real time with a quantum random number generator integrated into our control system to select the subsequent observable with a latency below 50 μs, which can be used to constrain contextual hidden-variable models that might describe our results. The state-recycling experimental procedure is resilient to noise and independent of the qutrit state, substantiating the fact that the contextual nature of quantum physics is connected to measurements and not necessarily to designated states. The use of extended sequences of quantum nondemolition measurements finds applications in the fields of sensing and quantum information.
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Affiliation(s)
- F M Leupold
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - M Malinowski
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - C Zhang
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - V Negnevitsky
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - A Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain
| | - J Alonso
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - J P Home
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
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12
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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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13
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Cabello A, Gu M, Gühne O, Xu ZP. Optimal Classical Simulation of State-Independent Quantum Contextuality. PHYSICAL REVIEW LETTERS 2018; 120:130401. [PMID: 29694184 DOI: 10.1103/physrevlett.120.130401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2017] [Revised: 02/06/2018] [Indexed: 06/08/2023]
Abstract
Simulating quantum contextuality with classical systems requires memory. A fundamental yet open question is what is the minimum memory needed and, therefore, the precise sense in which quantum systems outperform classical ones. Here, we make rigorous the notion of classically simulating quantum state-independent contextuality (QSIC) in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite QSIC set. We obtain the minimum memory needed to simulate arbitrary QSIC sets via classical systems under the assumption that the simulation should not contain any oracular information. In particular, we show that, while classically simulating two qubits tested with the Peres-Mermin set requires log_{2}24≈4.585 bits, simulating a single qutrit tested with the Yu-Oh set requires, at least, 5.740 bits.
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Affiliation(s)
- Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Mile Gu
- School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
- Complexity Institute, Nanyang Technological University, 18 Nanyang Drive, Singapore 637723, Singapore
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
| | - Zhen-Peng Xu
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China
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14
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Xiao Y, Xu ZP, Li Q, Xu JS, Sun K, Cui JM, Zhou ZQ, Su HY, Cabello A, Chen JL, Li CF, Guo GC. Experimental observation of quantum state-independent contextuality under no-signaling conditions. OPTICS EXPRESS 2018; 26:32-50. [PMID: 29328292 DOI: 10.1364/oe.26.000032] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Accepted: 12/09/2017] [Indexed: 06/07/2023]
Abstract
Contextuality, the impossibility of assigning context-independent measurement outcomes, is a critical resource for quantum computation and communication. No-signaling between successive measurements is an essential requirement that should be accomplished in any test of quantum contextuality and that is difficult to achieve in practice. Here, we introduce an optimal quantum state-independent contextuality inequality in which the deviation from the classical bound is maximal. We then experimentally test it using single photons generated from a defect in a bulk silicon carbide, while satisfying the requirement of no-signaling within the experimental error. Our results shed new light on the study of quantum contextuality under no-signaling conditions.
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15
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Abstract
The Klyachko, Can, Binicioglu, and Shumovsky (KCBS) inequality is an important contextuality inequality in three-level system, which has been demonstrated experimentally by using quantum states. Using the path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), tested the KCBS inequality and its geometrical form (Wright's inequality) in this work. The projection measurement has been implemented, the clear violations of the KCBS inequality and its geometrical form have been observed. This means that the contextuality inequality, which is commonly used in test of the conflict between quantum theory and noncontextual realism, may be used as a quantitative tool in classical optical coherence to describe correlation characteristics of the classical fields.
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16
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Liu BH, Hu XM, Chen JS, Huang YF, Han YJ, Li CF, Guo GC, Cabello A. Nonlocality from Local Contextuality. PHYSICAL REVIEW LETTERS 2016; 117:220402. [PMID: 27925740 DOI: 10.1103/physrevlett.117.220402] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2016] [Indexed: 06/06/2023]
Abstract
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.
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Affiliation(s)
- Bi-Heng Liu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, 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
| | - Xiao-Min Hu
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, 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
| | - Jiang-Shan Chen
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, 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, Chinese Academy of Sciences, 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
| | - Yong-Jian Han
- Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, 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, Chinese Academy of Sciences, 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, Chinese Academy of Sciences, 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
| | - Adán Cabello
- Departmento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
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Jerger M, Reshitnyk Y, Oppliger M, Potočnik A, Mondal M, Wallraff A, Goodenough K, Wehner S, Juliusson K, Langford NK, Fedorov A. Contextuality without nonlocality in a superconducting quantum system. Nat Commun 2016; 7:12930. [PMID: 27698351 PMCID: PMC5059491 DOI: 10.1038/ncomms12930] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2016] [Accepted: 08/11/2016] [Indexed: 12/03/2022] Open
Abstract
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with them. The Bell–Kochen–Specker theorem states that noncontextual realism cannot reproduce the measurement statistics of a single three-level quantum system (qutrit). Noncontextual realistic models may thus be tested using a single qutrit without relying on the notion of quantum entanglement in contrast to Bell inequality tests. It is challenging to refute such models experimentally, since imperfections may introduce loopholes that enable a realist interpretation. Here we use a superconducting qutrit with deterministic, binary-outcome readouts to violate a noncontextuality inequality while addressing the detection, individual-existence and compatibility loopholes. This evidence of state-dependent contextuality also demonstrates the fitness of superconducting quantum circuits for fault-tolerant quantum computation in surface-code architectures, currently the most promising route to scalable quantum computing. Tests of the Bell-Kochen-Specker theorem aim at showing that the measurement statistics of a single qutrit are incompatible with noncontextual realism. Here, the authors use a superconducting qutrit with deterministic readouts to violate a noncontextuality inequality, ruling out several loopholes.
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Affiliation(s)
- Markus Jerger
- ARC Centre of Excellence for Engineered Quantum Systems, The University of Queensland, St Lucia, Queensland 4072, Australia
| | - Yarema Reshitnyk
- School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland 4072, Australia
| | - Markus Oppliger
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Anton Potočnik
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Mintu Mondal
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | | | - Kenneth Goodenough
- QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft, The Netherlands
| | - Stephanie Wehner
- QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft, The Netherlands
| | - Kristinn Juliusson
- Quantronics group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, Gif-sur-Yvette 91191, France
| | - Nathan K Langford
- QuTech, Delft University of Technology, Lorentzweg 1, 2611 CJ Delft, The Netherlands.,Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
| | - Arkady Fedorov
- ARC Centre of Excellence for Engineered Quantum Systems, The University of Queensland, St Lucia, Queensland 4072, Australia.,School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland 4072, Australia
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18
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Time reversal and charge conjugation in an embedding quantum simulator. Nat Commun 2015; 6:7917. [PMID: 26239028 PMCID: PMC4532877 DOI: 10.1038/ncomms8917] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2015] [Accepted: 06/22/2015] [Indexed: 11/27/2022] Open
Abstract
A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be implemented in such a quantum system due to the linear character of quantum mechanics. Here, we present the experimental quantum simulation of such an unphysical operation beyond the regime of unitary and dissipative evolutions through the embedding of a quantum dynamics in the electronic multilevels of a 171Yb+ ion. We perform time reversal and charge conjugation, which are paradigmatic examples of antiunitary symmetry operators, in the evolution of a Majorana equation without the tomographic knowledge of the evolving state. Thus, these operations can be applied regardless of the system size. Our approach offers the possibility to add unphysical operations to the toolbox of quantum simulation, and provides a route to efficiently compute otherwise intractable quantities, such as entanglement monotones. Quantum simulation has the potential to enable experimentally studying problems which are not directly tractable in a laboratory or computationally. Here, the authors simulate the Majorana equation with a ytterbium ion, which requires them to simulate antiunitary and therefore unphysical operations.
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Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities. Sci Rep 2015; 5:11637. [PMID: 26109325 PMCID: PMC4480019 DOI: 10.1038/srep11637] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Accepted: 03/26/2015] [Indexed: 11/17/2022] Open
Abstract
Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While various proofs of such contextual behavior of quantum systems have been established, relatively little is known concerning the possibility to demonstrate this intriguing feature for indistinguishable particles. Here, we show in a simple and systematic manner that with projective measurements alone, it is possible to demonstrate quantum contextuality for such systems of arbitrary Hilbert space dimensions, including those corresponding to a qubit. Our demonstration is applicable to a single fermion as well as multiple fermions, and thus also a composite boson formed from an even number of fermions. In addition, our approach gives a clear demonstration of the intimate connection between complementarity and contextuality, two seemingly unrelated aspects of quantum theory.
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20
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Experimental certification of random numbers via quantum contextuality. Sci Rep 2014; 3:1627. [PMID: 23568082 PMCID: PMC4070742 DOI: 10.1038/srep01627] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Accepted: 03/22/2013] [Indexed: 11/20/2022] Open
Abstract
The intrinsic unpredictability of measurements in quantum mechanics can be used to produce genuine randomness. Here, we demonstrate a random number generator where the randomness is certified by quantum contextuality in connection with the Kochen-Specker theorem. In particular, we generate random numbers from measurements on a single trapped ion with three internal levels, and certify the generated randomness by showing a bound on the minimum entropy through observation of violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Concerning the test of the KCBS inequality, we close the detection efficiency loophole for the first time and make it relatively immune to the compatibility loophole. In our experiment, we generate 1 × 105 random numbers that are guaranteed to have 5.2 × 104 bits of minimum entropy with a 99% confidence level.
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Cabello A, Severini S, Winter A. Graph-theoretic approach to quantum correlations. PHYSICAL REVIEW LETTERS 2014; 112:040401. [PMID: 24580419 DOI: 10.1103/physrevlett.112.040401] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2013] [Indexed: 06/03/2023]
Abstract
Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number, and the fractional packing number of this subgraph, respectively. We also show that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body. This identifies these combinatorial notions as fundamental physical objects and provides a method for singling out experiments with quantum correlations on demand.
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Affiliation(s)
- Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Simone Severini
- Department of Computer Science, and Department of Physics and Astronomy, University College London, WC1E 6BT London, United Kingdom
| | - Andreas Winter
- ICREA and Física Teòrica: Informació i Fenomens Quàntics, Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain
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22
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Abstract
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3n). As an example, three-qutrit systems are investigated in detail.
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