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Zhang C, Zhang WH, Sekatski P, Bancal JD, Zwerger M, Yin P, Li GC, Peng XX, Chen L, Han YJ, Xu JS, Huang YF, Chen G, Li CF, Guo GC. Certification of Genuine Multipartite Entanglement with General and Robust Device-Independent Witnesses. PHYSICAL REVIEW LETTERS 2022; 129:190503. [PMID: 36399745 DOI: 10.1103/physrevlett.129.190503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Accepted: 09/28/2022] [Indexed: 06/16/2023]
Abstract
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected in the experiment, namely, device independently. However, it is difficult to certify genuine entanglement of practical multipartite states in this way, and even more difficult to quantify it, due to the difficulty in identifying optimal multipartite Bell inequalities and protocols tolerant to state impurity. In this Letter, we explore a general and robust device-independent method that can be applied to various realistic multipartite quantum states in arbitrary finite dimension, while merely relying on bipartite Bell inequalities. Our method allows us both to certify the presence of genuine multipartite entanglement and to quantify it. Several important classes of entangled states are tested with this method, leading to the detection of genuinely entangled states. We also certify genuine multipartite entanglement in weakly entangled Greenberger-Horne-Zeilinger states, showing that the method applies equally well to less standard states.
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Affiliation(s)
- Chao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Wen-Hao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Pavel Sekatski
- Department of Applied Physics, University of Geneva, Rue de l'École-de-Médecine, 1211 Geneva, Switzerland
| | - Jean-Daniel Bancal
- Université Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191 Gif-sur-Yvette, France
| | - Michael Zwerger
- Max Planck Institute for the Science of Light, Erlangen 91058, Germany
| | - Peng Yin
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Gong-Chu Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Xing-Xiang Peng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Lei Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yong-Jian Han
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yun-Feng Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Geng Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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Wu D, Zhao Q, Wang C, Huang L, Jiang YF, Bai B, Zhou Y, Gu XM, Liu FM, Mao YQ, Sun QC, Chen MC, Zhang J, Peng CZ, Zhu XB, Zhang Q, Lu CY, Pan JW. Closing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing. PHYSICAL REVIEW LETTERS 2022; 128:250401. [PMID: 35802432 DOI: 10.1103/physrevlett.128.250401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Revised: 04/20/2022] [Accepted: 06/06/2022] [Indexed: 06/15/2023]
Abstract
First proposed by Mayers and Yao, self-testing provides a certification method to infer the underlying physics of quantum experiments in a black-box scenario. Numerous demonstrations have been reported to self-test various types of entangled states. However, all the multiparticle self-testing experiments reported so far suffer from both detection and locality loopholes. Here, we report the first experimental realization of multiparticle entanglement self-testing closing the locality loophole in a photonic system, and the detection loophole in a superconducting system, respectively. We certify three-party and four-party GHZ states with at least 0.84(1) and 0.86(3) fidelities in a device-independent way. These results can be viewed as a meaningful advance in multiparticle loophole-free self-testing, and also significant progress on the foundations of quantum entanglement certification.
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Affiliation(s)
- 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Qi Zhao
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Can 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Liang Huang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yang-Fan Jiang
- Jinan Institute of Quantum Technology, Jinan 250101, China
| | - Bing Bai
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - You Zhou
- Key Laboratory for Information Science of Electromagnetic Waves (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Xue-Mei Gu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Feng-Ming 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Ying-Qiu Mao
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Qi-Chao Sun
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jun Zhang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Cheng-Zhi Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xiao-Bo Zhu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Qiang Zhang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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3
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Yin XF, Du Y, Fei YY, Zhang R, Liu LZ, Mao Y, Liu T, Hsieh MH, Li L, Liu NL, Tao D, Chen YA, Pan JW. Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver. PHYSICAL REVIEW LETTERS 2022; 128:110501. [PMID: 35363009 DOI: 10.1103/physrevlett.128.110501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Revised: 12/28/2021] [Accepted: 02/11/2022] [Indexed: 06/14/2023]
Abstract
The recognition of entanglement states is a notoriously difficult problem when no prior information is available. Here, we propose an efficient quantum adversarial bipartite entanglement detection scheme to address this issue. Our proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits, where a two-outcome measurement can be used to query a classical binary result about whether the input state is bipartite entangled or not. In principle, for an N-qubit quantum state, the runtime complexity of our proposal is O(poly(N)T) with T being the number of iterations. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states. Our work paves the way for using near-term quantum machines to tackle entanglement detection on multipartite entangled quantum systems.
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Affiliation(s)
- Xu-Fei Yin
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yuxuan Du
- JD Explore Academy, Beijing 101111, China
- School of Computer Science, Faculty of Engineering, University of Sydney, Sydney 2006, Australia
| | - Yue-Yang Fei
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Rui Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Li-Zheng Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yingqiu Mao
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Tongliang Liu
- School of Computer Science, Faculty of Engineering, University of Sydney, Sydney 2006, Australia
| | - Min-Hsiu Hsieh
- Hon Hai Quantum Computing Research Center, Taipei 114, Taiwan
| | - Li Li
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Nai-Le Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Dacheng Tao
- JD Explore Academy, Beijing 101111, China
- School of Computer Science, Faculty of Engineering, University of Sydney, Sydney 2006, Australia
| | - Yu-Ao Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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4
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Xu JM, Zhou Q, Yang YX, Cheng ZM, Xu XY, Ren ZC, Wang XL, Wang HT. Experimental self-testing for photonic graph states. OPTICS EXPRESS 2022; 30:101-111. [PMID: 35201184 DOI: 10.1364/oe.446154] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2021] [Accepted: 12/09/2021] [Indexed: 06/14/2023]
Abstract
Graph states-one of the most representative families of multipartite entangled states-are important resources for multiparty quantum communication, quantum error correction, and quantum computation. Device-independent certification of highly entangled graph states plays a prominent role in quantum information processing tasks. Here we have experimentally demonstrated device-independent certification for multipartite graph states by adopting the robust self-testing scheme based on scalable Bell inequalities. Specifically, the prepared multi-qubit Greenberger-Horne-Zeilinger (GHZ) states and linear cluster states achieve a high degree of Bell violation, which are beyond the nontrivial bounds of the robust self-testing scheme. Furthermore, our work paves the way to the device-independent certification of complex multipartite quantum states.
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Wu D, Zhao Q, Gu XM, Zhong HS, Zhou Y, Peng LC, Qin J, Luo YH, Chen K, Li L, Liu NL, Lu CY, Pan JW. Robust Self-Testing of Multiparticle Entanglement. PHYSICAL REVIEW LETTERS 2021; 127:230503. [PMID: 34936806 DOI: 10.1103/physrevlett.127.230503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Revised: 09/14/2021] [Accepted: 11/04/2021] [Indexed: 06/14/2023]
Abstract
Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Because of the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multiphoton genuinely entangled quantum states. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.
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Affiliation(s)
- 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Qi Zhao
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Xue-Mei Gu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Han-Sen Zhong
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - You Zhou
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore
| | - Li-Chao Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Jian Qin
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Yi-Han Luo
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Kai 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, 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
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
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Ding ZY, Zhou PF, Liu JX, Liu CC, Zhao M, Yang H, Fan XG, He J, Ye L. Experimental verification of the relationship between first-order coherence and linear steerability. OPTICS EXPRESS 2021; 29:40668-40676. [PMID: 34809401 DOI: 10.1364/oe.445991] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Accepted: 11/12/2021] [Indexed: 06/13/2023]
Abstract
Coherence and steerability are two essential characteristics of quantum systems. For a two-qubit state, the first-order coherence and the maximal violation of linear steering inequality are used to operationally measure the degree of coherence and steerability, respectively. Recently, a complementary relation between first-order coherence and linear steerability has been proposed. In this paper, we report an experimental verification of the complementary relation by preparing biphoton polarization entangled states in an all-optical setup. We propose an operable method for experimental measurement of the first-order coherence and linear steerability and calculate the purity of the initial states by reconstructing the density matrices of them. The experimental results coincide with the theoretical predictions very well, which provides a valuable reference for the application of optical quantum technology.
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Zhang WH, Zhang C, Chen Z, Peng XX, Xu XY, Yin P, Yu S, Ye XJ, Han YJ, Xu JS, Chen G, Li CF, Guo GC. Experimental Optimal Verification of Entangled States Using Local Measurements. PHYSICAL REVIEW LETTERS 2020; 125:030506. [PMID: 32745389 DOI: 10.1103/physrevlett.125.030506] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2020] [Accepted: 07/01/2020] [Indexed: 06/11/2023]
Abstract
The initialization of a quantum system into a certain state is a crucial aspect of quantum information science. While a variety of measurement strategies have been developed to characterize how well the system is initialized, for a given one, there is in general a trade-off between its efficiency and the accessible information of the quantum state. Conventional quantum state tomography can characterize unknown states while requiring exponentially expensive time-consuming postprocessing. Alternatively, recent theoretical breakthroughs show that quantum state verification provides a technique to quantify the prepared state with significantly fewer samples, especially for multipartite entangled states. In this Letter, we modify the original proposal to be robust to practical imperfections, and experimentally implement a scalable quantum state verification on two-qubit and four-qubit entangled states with nonadaptive local measurements. For all the tested states, the estimated infidelity is inversely proportional to the number of samples, which illustrates the power to characterize a quantum state with a small number of samples. Compared to the globally optimal strategy which requires nonlocal measurements, the efficiency in our experiment is only worse by a small constant factor (<2.5). We compare the performance difference between quantum state verification and quantum state tomography in an experiment to characterize a four-photon Greenberger-Horne-Zeilinger state, and the results indicate the advantage of quantum state verification in both the achieved efficiency and precision.
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Affiliation(s)
- Wen-Hao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhe Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xing-Xiang Peng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Peng Yin
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Shang Yu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiang-Jun Ye
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yong-Jian Han
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Geng Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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9
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Zhang A, Xie J, Xu H, Zheng K, Zhang H, Poon YT, Vedral V, Zhang L. Experimental Self-Characterization of Quantum Measurements. PHYSICAL REVIEW LETTERS 2020; 124:040402. [PMID: 32058739 DOI: 10.1103/physrevlett.124.040402] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Indexed: 06/10/2023]
Abstract
The accurate and reliable description of measurement devices is a central problem in both observing uniquely nonclassical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum tomography is the prevalent tool to characterize quantum detectors. However, such a characterization relies on accurately characterized probe states, rendering reliability of the characterization lost in circular argument. Here we report a self-characterization method of quantum measurements based on reconstructing the response range-the entirety of attainable measurement outcomes, eliminating the reliance on known states. We characterize two representative measurements implemented with photonic setups and obtain fidelities above 99.99% with the conventional tomographic reconstructions. This initiates range-based techniques in characterizing quantum systems and foreshadows novel device-independent protocols of quantum information applications.
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Affiliation(s)
- Aonan Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Jie Xie
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Huichao Xu
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- 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 (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Han Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Yiu-Tung Poon
- Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen, 518055, China
| | - Vlatko Vedral
- Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX13PU, United Kingdom
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Lijian Zhang
- National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation (Ministry of Education), College of Engineering and Applied Sciences and School of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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10
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Zhang WH, Chen G, Peng XX, Ye XJ, Yin P, Xu XY, Xu JS, Li CF, Guo GC. Experimental Realization of Robust Self-Testing of Bell State Measurements. PHYSICAL REVIEW LETTERS 2019; 122:090402. [PMID: 30932519 DOI: 10.1103/physrevlett.122.090402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Indexed: 06/09/2023]
Abstract
Bell state measurements, of which the eigenvectors are in an entangled form, are crucial resources in the construction of quantum networks. Therefore, device-independent certification of a Bell state measurement has significance in the quantum information process because it satisfies the exact demand on security. In this study, we implement a proof-of-concept experiment to certify a Bell state measurement device independently in an entanglement swapping process, namely, self-testing. Instead of preparing a tensor product of two singlets with four photons, multiplex encoding in polarization and spatial modes is utilized to produce two pairs of entangled qubits. As a result, we implement a full Bell state measurement and achieve a high degree of Bell violation on the remaining two qubits, which are required for nontrivial self-testing of a Bell state measurement. Furthermore, our results combine the correlations before and after the swapping; thus, the quality of the performed Bell state measurement can be precisely inferred.
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Affiliation(s)
- Wen-Hao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Geng Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xing-Xiang Peng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiang-Jun Ye
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Peng Yin
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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