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Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2019 Impact Factor: 2.502

Frontiers of Physics  2023, Vol. 18 Issue (3): 31302   https://doi.org/10.1007/s11467-022-1242-6
  本期目录
Sharing quantum nonlocality in star network scenarios
Tinggui Zhang1,2(), Naihuan Jing2,3, Shao-Ming Fei1,4,5
1. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
2. College of Sciences, Shanghai University, Shanghai 200444, China
3. Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA
4. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
5. Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany
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Abstract

The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.

Key wordsBell nonlocality    quantum network    nonlocality sharing    POVM measurements
收稿日期: 2022-10-19      出版日期: 2023-01-16
Corresponding Author(s): Tinggui Zhang   
 引用本文:   
. [J]. Frontiers of Physics, 2023, 18(3): 31302.
Tinggui Zhang, Naihuan Jing, Shao-Ming Fei. Sharing quantum nonlocality in star network scenarios. Front. Phys. , 2023, 18(3): 31302.
 链接本文:  
https://academic.hep.com.cn/fop/CN/10.1007/s11467-022-1242-6
https://academic.hep.com.cn/fop/CN/Y2023/V18/I3/31302
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1 Einstein A. , Podolsky B. , Rosen N. . Can quantum-mechanical description of physical reality be considered complete. Phys. Rev., 1935, 47(10): 777
https://doi.org/10.1103/PhysRev.47.777
2 Cao H. , Guo Z. . Characterizing Bell nonlocality and EPR steering. Sci. China Phys. Mech. Astron., 2019, 62(3): 30311
https://doi.org/10.1007/s11433-018-9279-4
3 Brunner N. , Cavalcanti D. , Pironio S. , Scarani V. , Wehner S. . Bell nonlocality. Rev. Mod. Phys., 2014, 86(2): 419
https://doi.org/10.1103/RevModPhys.86.419
4 Acín A. , Brunner N. , Gisin N. , Massar S. , Pironio S. , Scarani V. . Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett., 2007, 98(23): 230501
https://doi.org/10.1103/PhysRevLett.98.230501
5 Pironio S. , Acín A. , Massar S. , B. de la Giroday A. , N. Matsukevich D. , Maunz P. , Olmschenk S. , Hayes D. , Luo L. , A. Manning T. , Monroe C. . Random numbers certified by Bell’s theorem. Nature, 2010, 464(7291): 1021
https://doi.org/10.1038/nature09008
6 Colbeck R. , Renner R. . Free randomness can be amplified. Nat. Phys., 2012, 8(6): 450
https://doi.org/10.1038/nphys2300
7 H. Li M. , Zhang X. , Z. Liu W. , R. Zhao S. , Bai B. , Liu Y. , Zhao Q. , Peng Y. , Zhang J. , Zhang Y. , J. Munro W. , Ma X. , Zhang Q. , Fan J. , W. Pan J. . Experimental realization of device-independent quantum randomness expansion. Phys. Rev. Lett., 2021, 126(5): 050503
https://doi.org/10.1103/PhysRevLett.126.050503
8 Z. Liu W. , H. Li M. , Ragy S. , R. Zhao S. , Bai B. , Liu Y. , J. Brown P. , Zhang J. , Colbeck R. , Fan J. , Zhang Q. , W. Pan J. . Device-independent randomness expansion against quantum side information. Nat. Phys., 2021, 17(4): 448
https://doi.org/10.1038/s41567-020-01147-2
9 K. Shalm L. , Zhang Y. , C. Bienfang J. , Schlager C. , J. Stevens M. , D. Mazurek M. , Abellán C. , Amaya W. , W. Mitchell M. , A. Alhejji M. , Fu H. , Ornstein J. , P. Mirin R. , W. Nam S. , Knill E. . Device-independent randomness expansion with entangled photons. Nat. Phys., 2021, 17(4): 452
https://doi.org/10.1038/s41567-020-01153-4
10 Silva R. , Gisin N. , Guryanova Y. , Popescu S. . Multiple observers can share the nonlocality of half of an entangled pair by using optimal weak measurements. Phys. Rev. Lett., 2015, 114(25): 250401
https://doi.org/10.1103/PhysRevLett.114.250401
11 S. Bell J. . On the Einstein−Podolsky−Rosen paradox. Physics, 1964, 1(3): 195
https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
12 F. Clauser J. , A. Horne M. , Shimony A. , A. Holt R. . Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 1969, 23(15): 880
https://doi.org/10.1103/PhysRevLett.23.880
13 Mal S. , Majumdar A. , Home D. . Sharing of nonlocality of a single member of an entangled pair of qubits is not possible by more than two unbiased observers on the other wing. Mathematics, 2016, 4(3): 48
https://doi.org/10.3390/math4030048
14 Shenoy H. A. , Designolle S. , Hirsch F. , Silva R. , Gisin N. , Brunner N. . Unbounded sequence of observers exhibiting Einstein−Podolsky−Rosen steering. Phys. Rev. A, 2019, 99: 022317
https://doi.org/10.1103/PhysRevA.99.022317
15 Das D. , Ghosal A. , Sasmal S. , Mal S. , S. Majum-dar A. . Facets of bipartite nonlocality sharing by multiple observers via sequential measurements. Phys. Rev. A, 2019, 99(2): 022305
https://doi.org/10.1103/PhysRevA.99.022305
16 Datta S. , S. Majumdar A. . Sharing of nonlocal advantage of quantum coherence by sequential observers. Phys. Rev. A, 2018, 98(4): 042311
https://doi.org/10.1103/PhysRevA.98.042311
17 Ren C. , Feng T. , Yao D. , Shi H. , Chen J. , Zhou X. . Passive and active nonlocality sharing for a two-qubit system via weak measurements. Phys. Rev. A, 2019, 100(5): 052121
https://doi.org/10.1103/PhysRevA.100.052121
18 Kumari A. , K. Pan A. . Sharing nonlocality and nontrivial preparation contextuality using the same family of Bell expressions. Phys. Rev. A, 2019, 100(6): 062130
https://doi.org/10.1103/PhysRevA.100.062130
19 Saha S. , Das D. , Sasmal S. , Sarkar D. , Mukherjee K. , Roy A. , S. Bhattacharya S. . Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side. Quantum Inform. Process., 2019, 18(2): 42
https://doi.org/10.1007/s11128-018-2161-x
20 Mohan K. , Tavakoli A. , Brunner N. . Sequential random access codes and self-testing of quantum instruments. New J. Phys., 2019, 21: 083034
https://doi.org/10.1088/1367-2630/ab3773
21 J. Brown P. , Colbeck R. . Arbitrarily many independent observers can share the nonlocality of a single maximally entangled qubit pair. Phys. Rev. Lett., 2020, 125(9): 090401
https://doi.org/10.1103/PhysRevLett.125.090401
22 Zhang T. , M. Fei S. . Sharing quantum nonlocality and genuine nonlocality with independent observables. Phys. Rev. A, 2021, 103(3): 032216
https://doi.org/10.1103/PhysRevA.103.032216
23 Zhang T. , Luo Q. , Huang X. . Quantum Bell nonlocality cannot be shared under a special kind of bilateral measurements for high-dimensional quantum states. Quantum Inform. Process., 2022, 21(10): 350
https://doi.org/10.1007/s11128-022-03699-z
24 Mukherjee S. , K. Pan A. . Semi-device-independent certification of multiple unsharpness parameters through sequential measurements. Phys. Rev. A, 2021, 104(6): 062214
https://doi.org/10.1103/PhysRevA.104.062214
25 J. Hu M. , Y. Zhou Z. , M. Hu X. , F. Li C. , C. Guo G. , S. Zhang Y. . Observation of non-locality sharing among three observers with one entangled pair via optimal weak measurement. npj Quantum Inf., 2018, 4(1): 63
https://doi.org/10.1038/s41534-018-0115-x
26 Schiavon M. , Calderaro L. , Pittaluga M. , Vallone G. , Villoresi P. . Three-observer Bell inequality violation on a two-qubit entangled state. Quantum Sci. Technol., 2017, 2(1): 015010
https://doi.org/10.1088/2058-9565/aa62be
27 Feng T. , Ren C. , Tian Y. , Luo M. , Shi H. , Chen J. , Zhou X. . Observation of nonlocality sharing via not-so-weak measurements. Phys. Rev. A, 2020, 102(3): 032220
https://doi.org/10.1103/PhysRevA.102.032220
28 Cheng S. , Liu L. , J. Baker T. , J. W. Hall M. . Limitations on sharing Bell nonlocality between sequential pairs of observers. Phys. Rev. A, 2021, 104(6): L060201
https://doi.org/10.1103/PhysRevA.104.L060201
29 Cheng S. , Liu L. , J. Baker T. , J. W. Hall M. . Recycling qubits for the generation of Bell nonlocality between independent sequential observers. Phys. Rev. A, 2022, 105(2): 022411
https://doi.org/10.1103/PhysRevA.105.022411
30 Arute F. , Arya K. , Babbush R. , Bacon D. , C. Bardin J. . et al.. Quantum supremacy using a programmable superconducting processor. Nature, 2019, 574(7779): 505
https://doi.org/10.1038/s41586-019-1666-5
31 S. Zhong H. , Wang H. , H. Deng Y. , C. Chen M. , C. Peng L. , H. Luo Y. , Qin J. , Wu D. , Ding X. , Hu Y. , Hu P. , Y. Yang X. , J. Zhang W. , Li H. , Li Y. , Jiang X. , Gan L. , Yang G. , You L. , Wang Z. , Li L. , L. Liu N. , Y. Lu C. , W. Pan J. . Quantum computational advantage using photons. Science, 2020, 370(6523): 1460
https://doi.org/10.1126/science.abe8770
32 S. Zhong H. , H. Deng Y. , Qin J. , Wang H. , C. Chen M. , C. Peng L. , H. Luo Y. , Wu D. , Q. Gong S. , Su H. , Hu Y. , Hu P. , Y. Yang X. , J. Zhang W. , Li H. , Li Y. , Jiang X. , Gan L. , Yang G. , You L. , Wang Z. , Li L. , L. Liu N. , J. Renema J. , Y. Lu C. , W. Pan J. . Phase-programmable Gaussian Boson sampling using stimulated squeezed light. Phys. Rev. Lett., 2021, 127(18): 180502
https://doi.org/10.1103/PhysRevLett.127.180502
33 Gong M. , Wang S. , Zha C. , C. Chen M. , L. Huang H. . et al.. Quantum walks on a programmable two-dimensional 62-qubit superconducting processor. Science, 2021, 372(6545): 948
https://doi.org/10.1126/science.abg7812
34 Wu Y. , S. Bao W. , Cao S. , Chen F. , C. Chen M. . et al.. Strong quantum computational advantage using a superconducting quantum processor. Phys. Rev. Lett., 2021, 127(18): 180501
https://doi.org/10.1103/PhysRevLett.127.180501
35 M. Liang J. , Q. Shen S. , Li M. , M. Fei S. . Quantum algorithms for the generalized eigenvalue problem. Quantum Inform. Process., 2022, 21(1): 23
https://doi.org/10.1007/s11128-021-03370-z
36 M. Liang J. , J. Wei S. , M. Fei S. . Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems. Sci. China Phys. Mech. Astron., 2022, 65(5): 250313
https://doi.org/10.1007/s11433-021-1844-7
37 Branciard C. , Gisin N. , Pironio S. . Characterizing the nonlocal correlations created via entanglement swapping. Phys. Rev. Lett., 2010, 104(17): 170401
https://doi.org/10.1103/PhysRevLett.104.170401
38 Cavalcanti D. , L. Almeida M. , Scarani V. , Acín A. . Quantum networks reveal quantum nonlocality. Nat. Commun., 2011, 2(1): 184
https://doi.org/10.1038/ncomms1193
39 Branciard C. , Rosset D. , Gisin N. , Pironio S. . Bilocal versus nonbilocal correlations in entanglement-swapping experiments. Phys. Rev. A, 2012, 85(3): 032119
https://doi.org/10.1103/PhysRevA.85.032119
40 Tavakoli A. , Skrzypczyk P. , Cavalcanti D. , Acin A. . Nonlocal correlations in the star-network configuration. Phys. Rev. A, 2014, 90(6): 062109
https://doi.org/10.1103/PhysRevA.90.062109
41 X. Luo M. . Computationally efficient nonlinear Bell inequalities for quantum networks. Phys. Rev. Lett., 2018, 120(14): 140402
https://doi.org/10.1103/PhysRevLett.120.140402
42 O. Renou M. , Bäumer E. , Boreiri S. , Brunner N. , Gisin N. , Beigi S. . Genuine quantum nonlocality in the triangle network. Phys. Rev. Lett., 2019, 123(14): 140401
https://doi.org/10.1103/PhysRevLett.123.140401
43 Tavakoli A. , Pozas-Kerstjens A. , X. Luo M. , O. Renou M. . Bell nonlocality in networks. Rep. Prog. Phys., 2022, 85(5): 056001
https://doi.org/10.1088/1361-6633/ac41bb
44 Contreras-Tejada P. , Palazuelos C. , I. de Vicente J. . Genuine multipartite nonlocality is intrinsic to quantum networks. Phys. Rev. Lett., 2021, 126(4): 040501
https://doi.org/10.1103/PhysRevLett.126.040501
45 Y. Hsu L. , H. Chen C. . Exploring Bell nonlocality of quantum networks with stabilizing and logical operators. Phys. Rev. Res., 2021, 3(2): 023139
https://doi.org/10.1103/PhysRevResearch.3.023139
46 Yang L. , Qi X. , Hou J. . Nonlocal correlations in the tree-tensor-network configuration. Phys. Rev. A, 2021, 104(4): 042405
https://doi.org/10.1103/PhysRevA.104.042405
47 Pozas-Kerstjens A. , Gisin N. , Tavakoli A. . Full network nonlocality. Phys. Rev. Lett., 2022, 128(1): 010403
https://doi.org/10.1103/PhysRevLett.128.010403
48 O. Renou M. , Beigi S. . Nonlocality for generic networks. Phys. Rev. Lett., 2022, 128(6): 060401
https://doi.org/10.1103/PhysRevLett.128.060401
49 Hou W. , Liu X. , Ren C. . Network nonlocality sharing via weak measurements in the extended bilocal scenario. Phys. Rev. A, 2022, 105(4): 042436
https://doi.org/10.1103/PhysRevA.105.042436
50 Gisin N. , Mei Q. , Tavakoli A. , O. Renou M. , Brunner N. . All entangled pure quantum states violate the bilocality inequality. Phys. Rev. A, 2017, 96: 020304(R)
https://doi.org/10.1103/PhysRevA.96.020304
51 Andreoli F. , Carvacho G. , Santodonato L. , Chaves R. , Sciarrino F. . Maximal qubit violation of n-locality inequalities in a star-shaped quantum network. New J. Phys., 2017, 19(11): 113020
https://doi.org/10.1088/1367-2630/aa8b9b
52 I. de Vicente J. . Separability criteria based on the Bloch representation of density matrices. Quantum Inf. Comput., 2007, 7(7): 624
https://doi.org/10.26421/QIC7.7-5
53 Horodecki R. , Horodecki P. , Horodecki M. . Violating Bell inequality by mixed states: Necessary and sufficient condition. Phys. Lett. A, 1995, 200(5): 340
https://doi.org/10.1016/0375-9601(95)00214-N
54 Ren C. , Liu X. , Hou W. , Feng T. , Zhou X. . Nonlocality sharing for a three-qubit system via multilateral sequential measurements. Phys. Rev. A, 2022, 105(5): 052221
https://doi.org/10.1103/PhysRevA.105.052221
55 Sasmal S. , Das D. , Mal S. , S. Majumdar A. . Steering a single system sequentially by multiple observers. Phys. Rev. A, 2018, 98(1): 012305
https://doi.org/10.1103/PhysRevA.98.012305
56 Bera A. , Mal S. , Sen(De) A. , Sen U. . Witnessing bipartite entanglement sequentially by multiple observers. Phys. Rev. A, 2018, 98(6): 062304
https://doi.org/10.1103/PhysRevA.98.062304
57 G. Maity A. , Das D. , Ghosal A. , Roy A. , S. Majumdar A. . Detection of genuine tripartite entanglement by multiple sequential observers. Phys. Rev. A, 2020, 101(4): 042340
https://doi.org/10.1103/PhysRevA.101.042340
58 Datta S. , S. Majumdar A. . Sharing of nonlocal advantage of quantum coherence by sequential observers. Phys. Rev. A, 2018, 98(4): 042311
https://doi.org/10.1103/PhysRevA.98.042311
59 L. Hu M. , R. Wang J. , Fan H. . Limits on sequential sharing of nonlocal advantage of quantum coherence. Sci. China Phys. Mech. Astron., 2022, 65(6): 260312
https://doi.org/10.1007/s11433-022-1892-0
60 J. Curchod F. , Johansson M. , Augusiak R. , J. Hoban M. , Wittek P. , Acin A. . Unbounded randomness certification using sequences of measurements. Phys. Rev. A, 2017, 95(2): 020102
https://doi.org/10.1103/PhysRevA.95.020102
61 Roy S. , Bera A. , Mal S. , Sen(De) A. , Sen U. . Recycling the resource: Sequential usage of shared state in quantum teleportation with weak measurements. Phys. Lett. A, 2021, 392: 127143
https://doi.org/10.1016/j.physleta.2021.127143
62 Mohan K. , Tavakoli A. , Brunner N. . Sequential random access codes and self-testing of quantum measurement instruments. New J. Phys., 2019, 21(8): 083034
https://doi.org/10.1088/1367-2630/ab3773
63 F. Yan Y. , Zhou L. , Zhong W. , B. Sheng Y. . Measurement-device-independent quantum key distribution of multiple degrees of freedom of a single photon. Front. Phys., 2021, 16(1): 11501
https://doi.org/10.1007/s11467-020-1005-1
64 M. Xie Y. , S. Lu Y. , X. Weng C. , Y. Cao X. , Y. Jia Z. , Bao Y. , Wang Y. , Fu Y. , L. Yin H. , B. Chen Z. . Breaking the rate-loss bound of quantum key distribution with asynchronous two-photon interference. PRX Quantum, 2022, 3(2): 020315
https://doi.org/10.1103/PRXQuantum.3.020315
65 Gu J. , Y. Cao X. , Fu Y. , W. He Z. , J. Yin Z. , L. Yin H. , B. Chen Z. . Experimental measurement-device-independent type quantum key distribution with flawed and correlated sources. Sci. Bull. (Beijing), 2022, 67(21): 2167
https://doi.org/10.1016/j.scib.2022.10.010
66 L. Yin H. , Fu Y. , L. Li C. , X. Weng C. , H. Li B. , Gu J. , S. Lu Y. , Huang S. , B. Chen Z. . Experimental quantum secure network with digital signatures and encryption. Natl. Sci. Rev., 2022, nwac228
https://doi.org/10.1093/nsr/nwac228
67 D. Ye Z. , Pan D. , Sun Z. , G. Du C. , G. Yin L. , L. Long G. . Generic security analysis framework for quantum secure direct communication. Front. Phys., 2021, 16(2): 21503
https://doi.org/10.1007/s11467-020-1025-x
68 S. Mahato S. , K. Pan A. . Pan, Sharing nonlocality in a quantum network by unbounded sequential observers. Phys. Rev. A, 2022, 106: 042218
https://doi.org/10.1103/PhysRevA.106.042218
69 H. Wang J. , J. Wang Y. , J. Wang L. , Chen Q. . Network nonlocality sharing via weak measurements in the generalized star network configuration. Phys. Rev. A, 2022, 106: 052412
https://doi.org/10.1103/PhysRevA.106.052412
70 L. Mao Y.Li Z.D.A. Steffinlongo, B. Guo, B. Liu, S. Xu, N. Gisin, A. Tavakoli, and J. Fan, Recycling nonlocality in a quantum network, arXiv: 2202.04840 (2022)
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