1
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Xu L, Zhou M, Tao R, Zhong Z, Wang B, Cao Z, Xia H, Wang Q, Zhan H, Zhang A, Yu S, Xu N, Dong Y, Ren C, Zhang L. Resource-Efficient Direct Characterization of General Density Matrix. Phys Rev Lett 2024; 132:030201. [PMID: 38307054 DOI: 10.1103/physrevlett.132.030201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 11/27/2023] [Indexed: 02/04/2024]
Abstract
Sequential weak measurements allow for the direct extraction of individual density-matrix elements, rather than relying on global reconstruction of the entire density matrix, which opens a new avenue for the characterization of quantum systems. Nevertheless, extending the sequential scheme to multiqudit quantum systems is challenging due to the requirement of multiple coupling processes for each qudit and the lack of appropriate precision evaluation. To address these issues, we propose a resource-efficient scheme (RES) that directly characterizes the density matrix of general multiqudit systems while optimizing measurements and establishing a feasible estimation analysis. In the RES, an efficient observable of the quantum system is constructed such that a single meter state coupled to each qudit is sufficient to extract the corresponding density-matrix element. An appropriate model based on the statistical distribution of errors is utilized to evaluate the precision and feasibility of the scheme. We have experimentally applied the RES to the direct characterization of general single-photon qutrit states and two-photon entangled states. The results show that the RES outperforms sequential schemes in terms of efficiency and precision in both weak- and strong-coupling scenarios. This Letter sheds new light on the practical characterization of large-scale quantum systems and the investigation of their nonclassical properties.
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Affiliation(s)
- Liang Xu
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Mingti Zhou
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Runxia Tao
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Zhipeng Zhong
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Ben Wang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Zhiyong Cao
- School of Electronic Control, Chang'an University, Xi'an 710064, China
| | - Hongkuan Xia
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Qianyi Wang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Hao Zhan
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Aonan Zhang
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - Shang Yu
- Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
| | - Nanyang Xu
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Ying Dong
- College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, 310018, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Changliang Ren
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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2
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Yang YH, Zhang BB, Wang XL, Geng SJ, Chen PY. Characterizing an Uncertainty Diagram and Kirkwood-Dirac Nonclassicality Based on Discrete Fourier Transform. Entropy (Basel) 2023; 25:1075. [PMID: 37510021 PMCID: PMC10377937 DOI: 10.3390/e25071075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Revised: 07/13/2023] [Accepted: 07/14/2023] [Indexed: 07/30/2023]
Abstract
In this paper, we investigate an uncertainty diagram and Kirkwood-Dirac (KD) nonclassicality based on discrete Fourier transform (DFT) in a d-dimensional system. We first consider the uncertainty diagram of the DFT matrix, which is a transition matrix from basis A to basis B. Here, the bases A, B are not necessarily completely incompatible. We show that for the uncertainty diagram of the DFT matrix, there is no "hole" in the region of the (nA,nB) plane above and on the line nA+nB=d+1. Then, we present where the holes are in the region strictly below the line and above the hyperbola nAnB=d. Finally, we provide an alternative proof of the conjecture about KD nonclassicality based on DFT.
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Affiliation(s)
- Ying-Hui Yang
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
| | - Bing-Bing Zhang
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
| | - Xiao-Li Wang
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
| | - Shi-Jiao Geng
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
| | - Pei-Ying Chen
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
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3
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Lock EH, Lee J, Choi DS, Bedford RG, Karna SP, Roy AK. Materials Innovations for Quantum Technology Acceleration: A Perspective. Adv Mater 2023:e2201064. [PMID: 37021584 DOI: 10.1002/adma.202201064] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2022] [Revised: 01/16/2023] [Indexed: 06/19/2023]
Abstract
A broad perspective of quantum technology state of the art is provided and critical stumbling blocks for quantum technology development are identified. Innovations in demonstrating and understanding electron entanglement phenomena using bulk and low-dimensional materials and structures are summarized. Correlated photon-pair generation via processes such as nonlinear optics is discussed. Application of qubits to current and future high-impact quantum technology development is presented. Approaches for realizing unique qubit features for large-scale encrypted communication, sensing, computing, and other technologies are still evolving; thus, materials innovation is crucially important. A perspective on materials modeling approaches for quantum technology acceleration that incorporate physics-based AI/ML, integrated with quantum metrology is discussed.
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Affiliation(s)
- Evgeniya H Lock
- Materials Science and Technology Division, U. S. Naval Research Laboratory, Washington, DC, 20375, USA
| | - Jonghoon Lee
- Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/RXAN, 2179 12th St, WPAFB, OH, 45433, USA
- ARCTOS Technology Solutions, 1270 N Fairfield Rd, Beavercreek, OH, 45432, USA
| | - Daniel S Choi
- DEVCOM Army Research Laboratory, Weapons and Materials Research Directorate, FCDD-RLW, Aberdeen Proving Ground, Beavercreek, MD, 21015, USA
| | - Robert G Bedford
- Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/RXAN, 2179 12th St, WPAFB, OH, 45433, USA
| | - Shashi P Karna
- DEVCOM Army Research Laboratory, Weapons and Materials Research Directorate, FCDD-RLW, Aberdeen Proving Ground, Beavercreek, MD, 21015, USA
| | - Ajit K Roy
- Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/RXAN, 2179 12th St, WPAFB, OH, 45433, USA
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4
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Hei XL, Li PB, Pan XF, Nori F. Enhanced Tripartite Interactions in Spin-Magnon-Mechanical Hybrid Systems. Phys Rev Lett 2023; 130:073602. [PMID: 36867822 DOI: 10.1103/physrevlett.130.073602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2022] [Accepted: 01/23/2023] [Indexed: 06/18/2023]
Abstract
Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single nitrogen-vacancy (NV) center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons, and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive) to modulate the mechanical motion (such as the center-of-mass motion of a NV spin in diamond trapped in an electrical trap or a levitated micromagnet in a magnetic trap), we can obtain a tunable and strong spin-magnon-phonon coupling at the single quantum level, with up to 2 orders of magnitude enhancement for the tripartite coupling strength. This enables, for example, tripartite entanglement among solid-state spins, magnons, and mechanical motions in quantum spin-magnonics-mechanics with realistic experimental parameters. This protocol can be readily implemented with the well-developed techniques in ion traps or magnetic traps and could pave the way for general applications in quantum simulations and information processing based on directly and strongly coupled tripartite systems.
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Affiliation(s)
- Xin-Lei Hei
- Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Peng-Bo Li
- Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Xue-Feng Pan
- Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
- Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
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5
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Lupu-Gladstein N, Yilmaz YB, Arvidsson-Shukur DRM, Brodutch A, Pang AOT, Steinberg AM, Halpern NY. Negative Quasiprobabilities Enhance Phase Estimation in Quantum-Optics Experiment. Phys Rev Lett 2022; 128:220504. [PMID: 35714243 DOI: 10.1103/physrevlett.128.220504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2021] [Accepted: 03/21/2022] [Indexed: 06/15/2023]
Abstract
Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities-quantum extensions of probabilities-engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using PPA, we measure a wave plate's birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter's amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA's metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.
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Affiliation(s)
- Noah Lupu-Gladstein
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Y Batuhan Yilmaz
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | | | - Aharon Brodutch
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Arthur O T Pang
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Aephraim M Steinberg
- CQIQC and Department of Physics, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
| | - Nicole Yunger Halpern
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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6
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De Bièvre S. Complete Incompatibility, Support Uncertainty, and Kirkwood-Dirac Nonclassicality. Phys Rev Lett 2021; 127:190404. [PMID: 34797160 DOI: 10.1103/physrevlett.127.190404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2021] [Accepted: 10/08/2021] [Indexed: 06/13/2023]
Abstract
For quantum systems with a finite dimensional Hilbert space of states, we show that the complete incompatibility of two observables-a notion we introduce-is equivalent to the large support uncertainty of all states. The Kirkwood-Dirac (KD) quasiprobability distribution of a state-which depends on the choice of two observables-has emerged in quantum information theory as a tool for assessing nonclassical features of the state that can serve as a resource in quantum protocols. We apply our result to show that, when the two observables are completely incompatible, only states with minimal support uncertainty can be KD classical, all others being KD nonclassical. We illustrate our findings with examples.
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Affiliation(s)
- Stephan De Bièvre
- Univ. Lille, CNRS, Inria, UMR 8524 - Laboratoire Paul Painlevé, F-59000 Lille, France
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7
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Xu L, Xu H, Jiang T, Xu F, Zheng K, Wang B, Zhang A, Zhang L. Direct Characterization of Quantum Measurements Using Weak Values. Phys Rev Lett 2021; 127:180401. [PMID: 34767426 DOI: 10.1103/physrevlett.127.180401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Revised: 07/28/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
The time-symmetric formalism endows the weak measurement and its outcome, the weak value, with many unique features. In particular, it allows a direct tomography of quantum states without resorting to complicated reconstruction algorithms and provides an operational meaning to wave functions and density matrices. Here, we propose and experimentally demonstrate the direct tomography of a measurement apparatus by taking the backward direction of weak measurement formalism. Our protocol works rigorously with the arbitrary measurement strength, which offers improved accuracy and precision. The precision can be further improved by taking into account the completeness condition of the measurement operators, which also ensures the feasibility of our protocol for the characterization of the arbitrary quantum measurement. Our work provides new insight on the symmetry between quantum states and measurements, as well as an efficient method to characterize a measurement apparatus.
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Affiliation(s)
- Liang Xu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China
| | - Huichao Xu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Purple Mountain Laboratories, Nanjing, Jiangsu 211111, China
| | - Tao Jiang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Feixiang Xu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Kaimin Zheng
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Ben Wang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Aonan Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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8
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Zhou Y, Zhao J, Hay D, McGonagle K, Boyd RW, Shi Z. Direct Tomography of High-Dimensional Density Matrices for General Quantum States of Photons. Phys Rev Lett 2021; 127:040402. [PMID: 34355938 DOI: 10.1103/physrevlett.127.040402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Revised: 06/21/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
Quantum-state tomography is the conventional method used to characterize density matrices for general quantum states. However, the data acquisition time generally scales linearly with the dimension of the Hilbert space, hindering the possibility of dynamic monitoring of a high-dimensional quantum system. Here, we demonstrate a direct tomography protocol to measure density matrices of photons in the position basis through the use of a polarization-resolving camera, where the dimension of density matrices can be as large as 580×580 in our experiment. The use of the polarization-resolving camera enables parallel measurements in the position and polarization basis and as a result, the data acquisition time of our protocol does not increase with the dimension of the Hilbert space and is solely determined by the camera exposure time (on the order of 10 ms). Our method is potentially useful for the real-time monitoring of the dynamics of quantum states and paves the way for the development of high-dimensional, time-efficient quantum metrology techniques.
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Affiliation(s)
- Yiyu Zhou
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Jiapeng Zhao
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
| | - Darrick Hay
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Kendrick McGonagle
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
| | - Robert W Boyd
- The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
- Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Zhimin Shi
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
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9
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Chen MC, Li Y, Liu RZ, Wu D, Su ZE, Wang XL, Li L, Liu NL, Lu CY, Pan JW. Directly Measuring a Multiparticle Quantum Wave Function via Quantum Teleportation. Phys Rev Lett 2021; 127:030402. [PMID: 34328769 DOI: 10.1103/physrevlett.127.030402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
We propose a new method to directly measure a general multiparticle quantum wave function, a single matrix element in a multi-particle density matrix, by quantum teleportation. The density matrix element is embedded in a virtual logical qubit and is nondestructively teleported to a single physical qubit for readout. We experimentally implement this method to directly measure the wave function of a photonic mixed quantum state beyond a single photon using a single observable for the first time. Our method also provides an exponential advantage over the standard quantum state tomography in measurement complexity to fully characterize a sparse multiparticle quantum state.
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Affiliation(s)
- Ming-Cheng Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yuan Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Run-Ze Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Dian Wu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zu-En Su
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xi-Lin Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Nai-Le Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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10
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Ogawa K, Okazaki T, Kobayashi H, Nakanishi T, Tomita A. Direct measurement of ultrafast temporal wavefunctions. Opt Express 2021; 29:19403-19416. [PMID: 34266050 DOI: 10.1364/oe.423969] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 05/30/2021] [Indexed: 06/13/2023]
Abstract
The large capacity and robustness of information encoding in the temporal mode of photons is important in quantum information processing, in which characterizing temporal quantum states with high usability and time resolution is essential. We propose and demonstrate a direct measurement method of temporal complex wavefunctions for weak light at a single-photon level with subpicosecond time resolution. Our direct measurement is realized by ultrafast metrology of the interference between the light under test and self-generated monochromatic reference light; no external reference light or complicated post-processing algorithms are required. Hence, this method is versatile and potentially widely applicable for temporal state characterization.
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11
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Zhu J, Zhang P, Wang F, Wang Y, Li Q, Liu R, Wang J, Gao H, Li F. Experimentally measuring the mode indices of Laguerre-Gaussian beams by weak measurement. Opt Express 2021; 29:5419-5426. [PMID: 33726078 DOI: 10.1364/oe.416671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Accepted: 01/28/2021] [Indexed: 06/12/2023]
Abstract
As a special experimental technique, weak measurements extract very little information from the measured system and does not cause the measured state to collapse. When coupling the Laguerre-Gaussian (LG) state with a well-defined pre- and post-selected system of a weak measurement process, there will be an indirect interconnection between the expected value of coordinate operators of the final state and the mode indices of the measured LG state. The mode of the light is impacted very slightly after the weak measurement. Based on this we propose an experiment scheme and have managed to experimentally measure the mode indices of LG beams spanning from l = -6 to l = +6, p = 0 to p = +8 accurately with the final intensity distributions approximatly at their origin.
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12
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Yu S, Meng Y, Tang JS, Xu XY, Wang YT, Yin P, Ke ZJ, Liu W, Li ZP, Yang YZ, Chen G, Han YJ, Li CF, Guo GC. Experimental Investigation of Quantum PT-Enhanced Sensor. Phys Rev Lett 2020; 125:240506. [PMID: 33412046 DOI: 10.1103/physrevlett.125.240506] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2020] [Accepted: 11/06/2020] [Indexed: 06/12/2023]
Abstract
PT-symmetric theory is developed to extend quantum mechanics to a complex region, but it wins its great success first in classical systems, for example, optical waveguides and electric circuits, etc., because there are so many counterintuitive phenomena and striking applications, including unidirectional light transport, PT-enhanced sensors (one kind of exceptional-point-based sensor), and wireless power transfer. However, these phenomena and applications are mostly based on the ability to approach a PT-symmetric broken region, which makes it difficult to transfer them to the quantum regime, since the broken quantum PT-symmetric system has not been constructed effectively, until recently several methods have been raised. Here, we construct a quantum PT-symmetric system assisted by weak measurement, which can effectively transit from the unbroken region to the broken region. The full energy spectrum including the real and imaginary parts is directly measured using weak values. Furthermore, based on the ability of approaching a broken region, we for the first time translate the previously mentioned PT-enhanced sensor into the quantum version, and investigate its various features that are associated to the optimal conditions for sensitivity enhancement. In this experiment, we obtain an enhancement of 8.856 times over the conventional Hermitian sensor. Moreover, by separately detecting the real and imaginary parts of energy splitting, we can derive the additional information of the direction of perturbations. Our work paves the way of leading classical interesting PT phenomena and applications to their quantum counterparts. More generally, since the PT system is a subset of non-Hermitian systems, our work will be also helpful in the studies of general exception point in the quantum regime.
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Affiliation(s)
- Shang Yu
- 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, People's Republic of China
- Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou, 310000, People's Republic of China
| | - Yu Meng
- 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, People's Republic of China
| | - Jian-Shun Tang
- 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, People's Republic of China
| | - Xiao-Ye Xu
- 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, People's Republic of China
| | - Yi-Tao Wang
- 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, People's Republic of China
| | - Peng Yin
- 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, People's Republic of China
| | - Zhi-Jin Ke
- 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, People's Republic of China
| | - Wei 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, People's Republic of China
| | - Zhi-Peng 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, People's Republic of China
| | - Yuan-Ze Yang
- 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, People's Republic of China
| | - Geng Chen
- 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, People's Republic of China
| | - Yong-Jian Han
- 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, People's Republic of 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, People's Republic of 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, People's Republic of China
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13
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Sahoo SN, Chakraborti S, Pati AK, Sinha U. Quantum State Interferography. Phys Rev Lett 2020; 125:123601. [PMID: 33016750 DOI: 10.1103/physrevlett.125.123601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Accepted: 08/11/2020] [Indexed: 06/11/2023]
Abstract
Quantum state tomography (QST) has been the traditional method for characterization of an unknown state. Recently, many direct measurement methods have been implemented to reconstruct the state in a resource efficient way. In this Letter, we present an interferometric method, in which any qubit state, whether mixed or pure, can be inferred from the visibility, phase shift, and average intensity of an interference pattern using a single-shot measurement-hence, we call it quantum state interferography. This provides us with a "black box" approach to quantum state estimation, wherein, between the incidence of the photon and extraction of state information, we are not changing any conditions within the setup, thus giving us a true single shot estimation of the quantum state. In contrast, standard QST requires at least two measurements for pure state qubit and at least three measurements for mixed state qubit reconstruction. We then go on to show that QSI is more resource efficient than QST for quantification of entanglement in pure bipartite qubits. We experimentally implement our method with high fidelity using the polarization degree of freedom of light. An extension of the scheme to pure states involving d-1 interferograms for d-dimensional systems is also presented. Thus, the scaling gain is even more dramatic in the qudit scenario for our method, where, in contrast, standard QST, without any assumptions, scales roughly as d^{2}.
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Affiliation(s)
| | | | - Arun K Pati
- Quantum Information and Computation Group, Harish-Chandra Research Institute, HBNI, Allahabad 211019, India
| | - Urbasi Sinha
- Light and Matter Physics, Raman Research Institute, Bengaluru 560080, India
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14
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Arvidsson-Shukur DRM, Yunger Halpern N, Lepage HV, Lasek AA, Barnes CHW, Lloyd S. Quantum advantage in postselected metrology. Nat Commun 2020; 11:3775. [PMID: 32728082 PMCID: PMC7391714 DOI: 10.1038/s41467-020-17559-w] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 07/08/2020] [Indexed: 11/08/2022] Open
Abstract
In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantum-mechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool.
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Affiliation(s)
- David R M Arvidsson-Shukur
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK.
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
| | - Nicole Yunger Halpern
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, 02138, USA
- Department of Physics, Harvard University, Cambridge, MA, 02138, USA
| | - Hugo V Lepage
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Aleksander A Lasek
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Crispin H W Barnes
- Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, UK
| | - Seth Lloyd
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
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15
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Ho LB. Systematic errors in direct state measurements with quantum controlled measurements. J Phys B: At Mol Opt Phys 2020; 53:115501. [DOI: 10.1088/1361-6455/ab7881] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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16
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Zhang JD, Zhang ZJ, Cen LZ, Hu JY, Zhao Y. Super-resolved angular displacement estimation based upon a Sagnac interferometer and parity measurement. Opt Express 2020; 28:4320-4332. [PMID: 32122086 DOI: 10.1364/oe.384082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Accepted: 01/20/2020] [Indexed: 06/10/2023]
Abstract
Super-resolved angular displacement estimation is of crucial significance to the field of quantum information processing. Here we report an estimation protocol based on a Sagnac interferometer fed by a coherent state carrying orbital angular momentum. In a lossless scenario, through the use of parity measurement, our protocol can achieve a 4ℓ-fold super-resolved output with quantum number ℓ; meanwhile, a shot-noise-limited sensitivity saturating the quantum Cramér-Rao bound is reachable. We also consider the effects of several realistic factors, including nonideal state preparation, photon loss, and inefficient measurement. Finally, with mean photon number N¯=2.297 and ℓ = 1 taken, we experimentally demonstrate a super-resolved effect of angular displacement with a factor of 7.88.
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17
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Zhang S, Zhou Y, Mei Y, Liao K, Wen YL, Li J, Zhang XD, Du S, Yan H, Zhu SL. δ-Quench Measurement of a Pure Quantum-State Wave Function. Phys Rev Lett 2019; 123:190402. [PMID: 31765181 DOI: 10.1103/physrevlett.123.190402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Indexed: 06/10/2023]
Abstract
The measurement of a quantum state wave function not only acts as a fundamental part in quantum physics but also plays an important role in developing practical quantum technologies. Conventional quantum state tomography has been widely used to estimate quantum wave functions, which usually requires complicated measurement techniques. The recent weak-value-based quantum measurement circumvents this resource issue but relies on an extra pointer space. Here, we theoretically propose and then experimentally demonstrate a direct and efficient measurement strategy based on a δ-quench probe: by quenching its complex probability amplitude one by one (δ quench) in the given basis, we can directly obtain the quantum wave function of a pure ensemble by projecting the quenched state onto a postselection state. We confirm its power by experimentally measuring photonic complex temporal wave functions. This new method is versatile and can find applications in quantum information science and engineering.
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Affiliation(s)
- Shanchao Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yiru Zhou
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yefeng Mei
- Department of Physics & William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong S.A.R., China
| | - Kaiyu Liao
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Yong-Li Wen
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Jianfeng Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Xin-Ding Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Shengwang Du
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
- Department of Physics & William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong S.A.R., China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement and SPTE, South China Normal University, Guangzhou 510006, China
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
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18
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Pan WW, Xu XY, Kedem Y, Wang QQ, Chen Z, Jan M, Sun K, Xu JS, Han YJ, Li CF, Guo GC. Direct Measurement of a Nonlocal Entangled Quantum State. Phys Rev Lett 2019; 123:150402. [PMID: 31702297 DOI: 10.1103/physrevlett.123.150402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2019] [Revised: 06/24/2019] [Indexed: 06/10/2023]
Abstract
Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen et al. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.
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Affiliation(s)
- Wei-Wei Pan
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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
| | - Yaron Kedem
- Department of Physics, Stockholm University, AlbaNova University Center, 106 91 Stockholm, Sweden
| | - Qin-Qin Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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
| | - Zhe Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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
| | - Munsif Jan
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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
| | - Kai Sun
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 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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19
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Zhu J, Zhang P, Li Q, Wang F, Wang C, Zhou Y, Wang J, Gao H, Kwek LC, Li F. Measuring the Topological Charge of Orbital Angular Momentum Beams by Utilizing Weak Measurement Principle. Sci Rep 2019; 9:7993. [PMID: 31142778 PMCID: PMC6541590 DOI: 10.1038/s41598-019-44465-z] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2018] [Accepted: 05/17/2019] [Indexed: 11/09/2022] Open
Abstract
According to the principle of weak measurement, when coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there will be an indirect coupling between position and topological charge (TC) of OAM state. Based on this we propose an experiment scheme and experimentally measure the TC of OAM beams from -14 to 14 according to the weak measurement principle. After the experiment the intrinsic OAM of the beams changed very little. Weak measurement, Topological Charge, OAM beams.
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Affiliation(s)
- Jing Zhu
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China.,Center for Quantum Technologies, National University of Singapore, Singapore, 117543, Singapore
| | - Pei Zhang
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China. .,MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China.
| | - Qichang Li
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Feiran Wang
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Chenhui Wang
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Yingnan Zhou
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Jinwen Wang
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Hong Gao
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China
| | - Leong Chuan Kwek
- Center for Quantum Technologies, National University of Singapore, Singapore, 117543, Singapore.
| | - Fuli Li
- Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Science, Xi'an Jiaotong University, Xi'an, 710049, China
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20
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Chen JS, Hu MJ, Hu XM, Liu BH, Huang YF, Li CF, Guo CG, Zhang YS. Experimental realization of sequential weak measurements of non-commuting Pauli observables. Opt Express 2019; 27:6089-6097. [PMID: 30876202 DOI: 10.1364/oe.27.006089] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2018] [Accepted: 01/13/2019] [Indexed: 06/09/2023]
Abstract
Sequential weak measurements of non-commuting observables are not only fundamentally interesting in terms of quantum measurement but also show potential in various applications. Previously reported methods, however, can only make limited sequential weak measurements experimentally. In this article, we propose the realization of sequential measurements of non-commuting Pauli observables and experimentally demonstrate for the first time the measurement of sequential weak values of three non-commuting Pauli observables using genuine single photons.
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21
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Chen MC, Liu C, Luo YH, Huang HL, Wang BY, Wang XL, Li L, Liu NL, Lu CY, Pan JW. Experimental demonstration of quantum pigeonhole paradox. Proc Natl Acad Sci U S A 2019; 116:1549-52. [PMID: 30635427 DOI: 10.1073/pnas.1815462116] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We experimentally demonstrate that when three single photons transmit through two polarization channels, in a well-defined pre- and postselected ensemble, there are no two photons in the same polarization channel by weak-strength measurement, a counterintuitive quantum counting effect called the quantum pigeonhole paradox. We further show that this effect breaks down in second-order measurement. These results indicate the existence of the quantum pigeonhole paradox and its operating regime.
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23
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Calderaro L, Foletto G, Dequal D, Villoresi P, Vallone G. Direct Reconstruction of the Quantum Density Matrix by Strong Measurements. Phys Rev Lett 2018; 121:230501. [PMID: 30576212 DOI: 10.1103/physrevlett.121.230501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Indexed: 06/09/2023]
Abstract
New techniques based on weak measurements have recently been introduced to the field of quantum state reconstruction. Some of them allow the direct measurement of each matrix element of an unknown density operator and need only O(d) different operations, compared to d^{2} linearly independent projectors in the case of standard quantum state tomography, for the reconstruction of an arbitrary mixed state. However, due to the weakness of these couplings, these protocols are approximated and prone to large statistical errors. We propose a method which is similar to the weak measurement protocols but works regardless of the coupling strength: our protocol is not approximated and thus improves the accuracy and precision of the results with respect to weak measurement schemes. We experimentally apply it to the polarization state of single photons and compare the results to those of preexisting methods for different values of the coupling strength. Our results show that our method outperforms previous proposals in terms of accuracy and statistical errors.
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Affiliation(s)
- Luca Calderaro
- Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo 6B, 35131 Padova, Italy
- Centro di Ateneo di Studi e Attività Spaziali "Giuseppe Colombo", Università di Padova, via Venezia 15, 35131 Padova, Italy
| | - Giulio Foletto
- Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo 6B, 35131 Padova, Italy
| | - Daniele Dequal
- Matera Laser Ranging Observatory, Agenzia Spaziale Italiana, Matera 75100, Italy
| | - Paolo Villoresi
- Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo 6B, 35131 Padova, Italy
- Istituto di Fotonica e Nanotecnologie, CNR, via Trasea 7, 35131 Padova, Italy
| | - Giuseppe Vallone
- Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo 6B, 35131 Padova, Italy
- Istituto di Fotonica e Nanotecnologie, CNR, via Trasea 7, 35131 Padova, Italy
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Bandyopadhyay S, Laha S, Bhattacharya U, Dutta A. Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath. Sci Rep 2018; 8:11921. [PMID: 30093653 PMCID: PMC6085341 DOI: 10.1038/s41598-018-30377-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Accepted: 07/19/2018] [Indexed: 11/10/2022] Open
Abstract
We explore the possibility of dynamical quantum phase transitions (DQPTs) occurring during the temporal evolution of a quenched transverse field Ising chain coupled to a particle loss type of bath (local in Jordan-Wigner fermion space) using two versions of the Loschmidt overlap (LO), namely, the fidelity induced LO and the interferometric phase induced LO. The bath, on the one hand, dictates the dissipative evolution following a sudden quench and on the other, plays a role in dissipative mixed state preparation in the later part of the study. During a dissipative evolution following a sudden quench, no trace of DQPTs are revealed in both the fidelity and the interferometric phase approaches; however, remarkably the interferometric phase approach reveals the possibility of inter-steady state DQPTs in passage from one steady state to the other when the system is subjected to a quench after having reached the first steady state. We further probe the occurrences of DQPTs when the system evolves unitarily after being prepared in a mixed state of engineered purity by ramping the transverse field in a linear fashion in the presence of the bath. In this case though the fidelity approach fails to indicate any DQPT, the interferometric approach indeed unravels the possibility of occurrence of DQPTs which persists even up to a considerable loss of purity of the engineered initial state as long as a constraint relation involving the dissipative coupling and ramping time (rate) is satisfied. This constraint relation also marks the boundary between two dynamically inequivalent phases; in one the LO vanishes for the critical momentum mode (and hence DQPTs exist) while in the other no such critical mode can exist and hence the LO never vanishes.
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Affiliation(s)
| | - Sudarshana Laha
- Department of Physics, Indian Institute of Technology, Kanpur, 208016, India
| | - Utso Bhattacharya
- Department of Physics, Indian Institute of Technology, Kanpur, 208016, India
| | - Amit Dutta
- Department of Physics, Indian Institute of Technology, Kanpur, 208016, India
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Piacentini F, Avella A, Gramegna M, Lussana R, Villa F, Tosi A, Brida G, Degiovanni IP, Genovese M. Investigating the Effects of the Interaction Intensity in a Weak Measurement. Sci Rep 2018; 8:6959. [PMID: 29725051 PMCID: PMC5934410 DOI: 10.1038/s41598-018-25156-7] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2017] [Accepted: 04/13/2018] [Indexed: 11/09/2022] Open
Abstract
Measurements are crucial in quantum mechanics, for fundamental research as well as for applicative fields like quantum metrology, quantum-enhanced measurements and other quantum technologies. In the recent years, weak-interaction-based protocols like Weak Measurements and Protective Measurements have been experimentally realized, showing peculiar features leading to surprising advantages in several different applications. In this work we analyze the validity range for such measurement protocols, that is, how the interaction strength affects the weak value extraction, by measuring different polarization weak values on heralded single photons. We show that, even in the weak interaction regime, the coupling intensity limits the range of weak values achievable, setting a threshold on the signal amplification effect exploited in many weak measurement based experiments.
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Affiliation(s)
- Fabrizio Piacentini
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Alessio Avella
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Marco Gramegna
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Rudi Lussana
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Federica Villa
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Alberto Tosi
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
| | - Giorgio Brida
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Ivo Pietro Degiovanni
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Marco Genovese
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy.
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Qin L, Wang Z, Zhang C, Li XQ. Direct measurement of the quantum state of photons in a cavity. Opt Express 2018; 26:7034-7042. [PMID: 29609389 DOI: 10.1364/oe.26.007034] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Accepted: 12/18/2017] [Indexed: 06/08/2023]
Abstract
We propose a scheme to measure the quantum state of photons in a cavity. The proposal is based on the concept of quantum weak values and applies equally well to both the solid-state circuit and atomic cavity quantum electrodynamics (QED) systems. The proposed scheme allows us to access directly the superposition components in Fock state basis, rather than the Wigner function as usual in phase space. Moreover, the separate access feature held in the direct scheme does not require a global reconstruction for the quantum state, which provides a particular advantage beyond the conventional method of quantum state tomography.
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Kim Y, Kim YS, Lee SY, Han SW, Moon S, Kim YH, Cho YW. Direct quantum process tomography via measuring sequential weak values of incompatible observables. Nat Commun 2018; 9:192. [PMID: 29335489 DOI: 10.1038/s41467-017-02511-2] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2017] [Accepted: 12/06/2017] [Indexed: 11/09/2022] Open
Abstract
The weak value concept has enabled fundamental studies of quantum measurement and, recently, found potential applications in quantum and classical metrology. However, most weak value experiments reported to date do not require quantum mechanical descriptions, as they only exploit the classical wave nature of the physical systems. In this work, we demonstrate measurement of the sequential weak value of two incompatible observables by making use of two-photon quantum interference so that the results can only be explained quantum physically. We then demonstrate that the sequential weak value measurement can be used to perform direct quantum process tomography of a qubit channel. Our work not only demonstrates the quantum nature of weak values but also presents potential new applications of weak values in analyzing quantum channels and operations.
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Thekkadath GS, Saaltink RY, Giner L, Lundeen JS. Determining Complementary Properties with Quantum Clones. Phys Rev Lett 2017; 119:050405. [PMID: 28949711 DOI: 10.1103/physrevlett.119.050405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Indexed: 06/07/2023]
Abstract
In a classical world, simultaneous measurements of complementary properties (e.g., position and momentum) give a system's state. In quantum mechanics, measurement-induced disturbance is largest for complementary properties and, hence, limits the precision with which such properties can be determined simultaneously. It is tempting to try to sidestep this disturbance by copying the system and measuring each complementary property on a separate copy. However, perfect copying is physically impossible in quantum mechanics. Here, we investigate using the closest quantum analog to this copying strategy, optimal cloning. The coherent portion of the generated clones' state corresponds to "twins" of the input system. Like perfect copies, both twins faithfully reproduce the properties of the input system. Unlike perfect copies, the twins are entangled. As such, a measurement on both twins is equivalent to a simultaneous measurement on the input system. For complementary observables, this joint measurement gives the system's state, just as in the classical case. We demonstrate this experimentally using polarized single photons.
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Affiliation(s)
- G S Thekkadath
- Department of Physics, Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - R Y Saaltink
- Department of Physics, Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - L Giner
- Department of Physics, Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - J S Lundeen
- Department of Physics, Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
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Piacentini F, Avella A, Levi MP, Gramegna M, Brida G, Degiovanni IP, Cohen E, Lussana R, Villa F, Tosi A, Zappa F, Genovese M. Measuring Incompatible Observables by Exploiting Sequential Weak Values. Phys Rev Lett 2016; 117:170402. [PMID: 27824450 DOI: 10.1103/physrevlett.117.170402] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Indexed: 06/06/2023]
Abstract
One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.
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Affiliation(s)
- F Piacentini
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - A Avella
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - M P Levi
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - M Gramegna
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | - G Brida
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy
| | | | - E Cohen
- Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - R Lussana
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - F Villa
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - A Tosi
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - F Zappa
- Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - M Genovese
- INRIM, Strada delle Cacce 91, I-10135 Torino, Italy and INFN, Via P. Giuria 1, I-10125 Torino, Italy
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