ISSN 0253-2778

CN 34-1054/N

Open AccessOpen Access JUSTC Physics 04 August 2022

Twenty years of quantum contextuality at USTC

Cite this:
https://doi.org/10.52396/JUSTC-2022-0073
More Information
  • Author Bio:

    Zheng-Hao Liu received his Ph.D. degree from the University of Science and Technology of China in 2022. He was a laureate of the Wang Daheng Optical Award in 2021, the Outstanding Doctoral Dissertation of USTC in 2022, and the national Ph.D. fellowship of China in 2021. His research interest is optical tests of quantum foundations and quantum computing. Further information about him is available at https://manekimeow.github.io/

    Jin-Shi Xu is a Professor at the University of Science and Technology of China (USTC). He received his Ph.D. degree from USTC in 2009. His research field is quantum optics and quantum information. He is now focusing on optical quantum simulation and constructing spin-photon interfaces

    Chuan-Feng Li is a Professor at the University of Science and Technology of China (USTC). He received his Ph.D. degree from USTC in 1999. His research field is quantum optics and quantum information. He is now focusing on constructing quantum network and exploring quantum physics with quantum technology

  • Corresponding author: E-mail: jsxu@ustc.edu.cn; E-mail: cfli@ustc.edu.cn
  • Received Date: 30 April 2022
  • Accepted Date: 11 July 2022
  • Available Online: 04 August 2022
  • Quantum contextuality is one of the most perplexing and peculiar features of quantum mechanics. Concisely, it refers to the observation that the result of a single measurement in quantum mechanics depends on the set of joint measurements actually performed. The study of contextuality has a long history at the University of Science and Technology of China (USTC). Here we review the theoretical and experimental advances in this direction achieved at USTC over the last twenty years. We start by introducing the renowned simplest proof of state-independent contextuality. We then present several experimental tests of quantum versus noncontextual theories with photons. Finally, we discuss the investigation of the role of contextuality in general quantum information science and its application in quantum computation.
    Contextuality causes the result of a quantum measurement to depend on the whole setof co-measured observables. Figure courtesy of Siyuan Ma.
    Quantum contextuality is one of the most perplexing and peculiar features of quantum mechanics. Concisely, it refers to the observation that the result of a single measurement in quantum mechanics depends on the set of joint measurements actually performed. The study of contextuality has a long history at the University of Science and Technology of China (USTC). Here we review the theoretical and experimental advances in this direction achieved at USTC over the last twenty years. We start by introducing the renowned simplest proof of state-independent contextuality. We then present several experimental tests of quantum versus noncontextual theories with photons. Finally, we discuss the investigation of the role of contextuality in general quantum information science and its application in quantum computation.
    • The research advances regarding quantum contextuality at USTC in the new century are discussed.
    • The review presents both theoretical and experimental progresses, with an insight into quantum contextuality’s application in quantum information and quantum computing.
    • The fruitful study of quantum contextuality at USTC signifies its spearheading role in the exploration of quantum science.

  • loading
  • [1]
    Shor P W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Review, 1999, 41: 303–332. doi: 10.1137/S0036144598347011
    [2]
    Zhong H S, Wang H, Deng Y H, et al. Quantum computational advantage using photons. Science, 2020, 370: 1460–1463. doi: 10.1126/science.abe8770
    [3]
    Arrazola J, Bergholm V, Brádler K, et al. Quantum circuits with many photons on a programmable nanophotonic chip. Nature, 2021, 591: 54–60. doi: 10.1038/s41586-021-03202-1
    [4]
    Zhong H S, Deng Y H, Qin J, et al. Phase-programmable Gaussian boson sampling using stimulated squeezed light. Physical Review Letters, 2021, 127: 180502. doi: 10.1103/PhysRevLett.127.180502
    [5]
    Aaronson S, Arkhipov A. The computational complexity of linear optics. In: STOC ’11: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing. San Jose, USA: Association for Computing Machinery, 2011: 333–342.
    [6]
    Hamilton C S, Kruse R, Sansoni L, et al. Gaussian boson sampling. Physical Review Letters, 2017, 119: 170501. doi: 10.1103/PhysRevLett.119.170501
    [7]
    Gottesman D. The Heisenberg representation of quantum computers. [2022-03-01]. https://arxiv.org/abs/quant-ph/9807006.
    [8]
    Braunstein S L, van Loock P. Quantum information with continuous variables. Reviews of Modern Physics, 2005, 77: 513–577. doi: 10.1103/RevModPhys.77.513
    [9]
    Greenberger D M, Horne M A, Zeilinger A. Going beyond Bell’s theorem. In: Kafatos M editor. Bell’s Theorem, Quantum Theory and Conceptions of the Universe. AG, Switzerland: Springer, 1989: 69–72.
    [10]
    Hardy L. Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. Physical Review Letters, 1992, 68: 2981–2984. doi: 10.1103/PhysRevLett.68.2981
    [11]
    Leifer M S, Spekkens R W. Pre-and post-selection paradoxes and contextuality in quantum mechanics. Physical Review Letters, 2005, 95: 200405. doi: 10.1103/PhysRevLett.95.200405
    [12]
    Yu S, Oh C H, Quantum pigeonhole effect, Cheshire cat and contextuality. [2022-03-01]. https://arxiv.org/abs/1408.2477.
    [13]
    Abramsky S, Barbosa R S, Kishida K,et al. Contextuality, cohomology and paradox. In: Kreutzer S, editor. 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Dagstuhl, Germany: Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2015: 211–228.
    [14]
    Waegell M, Tollaksen J. Contextuality, pigeonholes, Cheshire cats, mean kings, and weak values. Quantum Studies: Mathematics and Foundations, 2018, 5: 325–349. doi: 10.1007/s40509-017-0127-9
    [15]
    Liu Z H, Pan W W, Xu X Y, et al. Experimental exchange of grins between quantum Cheshire cats. Nature Communications, 2020, 11: 3006. doi: 10.1038/s41467-020-16761-0
    [16]
    Howard M, Wallman J, Veitch V, et al. Contextuality supplies the “magic” for quantum computation. Nature, 2014, 510: 351–355. doi: 10.1038/nature13460
    [17]
    Spekkens R W. Negativity and contextuality are equivalent notions of nonclassicality. Physical Review Letters, 2008, 101: 020401. doi: 10.1103/PhysRevLett.101.020401
    [18]
    Raussendorf R. Contextuality in measurement-based quantum computation. Physical Review A, 2013, 88: 022322. doi: 10.1103/PhysRevA.88.022322
    [19]
    Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete? Physical Review, 1935, 47: 777–780. doi: 10.1103/PhysRev.47.777
    [20]
    Kochen S, Specker S. The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 1967, 17: 59–87.
    [21]
    Yu S, Oh C H. State-independent proof of Kochen-Specker theorem with 13 rays. Physical Review Letters, 2012, 108: 030402. doi: 10.1103/PhysRevLett.108.030402
    [22]
    Cabello A, Kleinmann M, Portillo J R. Quantum state-independent contextuality requires 13 rays. Journal of Physics A: Mathematical and Theoretical, 2016, 49: 38LT01. doi: 10.1088/1751-8113/49/38/38LT01
    [23]
    Huang Y F, Li C F, Zhang Y S, et al. Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters, 2003, 90: 250401. doi: 10.1103/PhysRevLett.90.250401
    [24]
    Flamini F, Spagnolo N, Sciarrino F. Photonic quantum information processing: A review. Reports on Progress in Physics, 2018, 82 (1): 016001. doi: 10.1088/1361-6633/aad5b2
    [25]
    Budroni C, Cabello A, Gühne O, et al. Quantum contextuality. [2022-03-15]. https://doi.org/10.48550/arXiv.2102.13036.
    [26]
    Thompson J, Kurzyński P, Lee S Y, et al. Recent advances in contextuality tests. Open Systems & Information Dynamics, 2016, 23: 1650009. doi: 10.1142/S1230161216500098
    [27]
    Cabello A, Severini S, Winter A. Graph-theoretic approach to quantum correlations. Physical Review Letters, 2014, 112: 040401. doi: 10.1103/PhysRevLett.112.040401
    [28]
    Xu Z P, Yu X D, Kleinmann M. State-independent quantum contextuality with projectors of nonunit rank. New Journal of Physics, 2021, 23: 043025. doi: 10.1088/1367-2630/abe6e3
    [29]
    Fine A. Hidden variables, joint probability, and the Bell inequalities. Physical Review Letters, 1982, 48: 291. doi: 10.1103/PhysRevLett.48.291
    [30]
    Cabello A, Estebaranz J M, García-Alcaine G. Bell-Kochen-Specker theorem: A proof with 18 vectors. Physics Letters A, 1996, 212: 183–187. doi: 10.1016/0375-9601(96)00134-X
    [31]
    Xu Z P, Chen J L, Gühne O. Proof of the Peres conjecture for contextuality. Physical Review Letters, 2020, 124: 230401. doi: 10.1103/PhysRevLett.124.230401
    [32]
    Uijlen S, Westerbaan B. A Kochen-Specker system has at least 22 vectors. New Generation Computing, 2016, 34: 3–23. doi: 10.1007/s00354-016-0202-5
    [33]
    Peres A. Two simple proofs of the Kochen-Specker theorem. Journal of Physics A: Mathematical and General, 1991, 24: L175. doi: 10.1088/0305-4470/24/4/003
    [34]
    Cabello A. Experimentally testable state-independent quantum contextuality. Physical Review Letters, 2008, 101: 210401. doi: 10.1103/PhysRevLett.101.210401
    [35]
    Lovász L. On the Shannon capacity of a graph. IEEE Transactions on Information Theory, 1979, 25: 1–7. doi: 10.1109/TIT.1979.1055985
    [36]
    Cabello A. Simple method for experimentally testing any form of quantum contextuality. Physical Review A, 2016, 93: 032102. doi: 10.1103/PhysRevA.93.032102
    [37]
    Cañas G, Acuña E, Cariñe J, et al. Experimental demonstration of the connection between quantum contextuality and graph theory. Physical Review A, 2016, 94: 012337. doi: 10.1103/PhysRevA.94.012337
    [38]
    Xiao Y, Xu Z P, Li Q, et al. Experimental observation of quantum state-independent contextuality under no-signaling conditions. Optics Express, 2018, 26: 32. doi: 10.1364/OE.26.000032
    [39]
    Liu Z H, Meng H X, Xu Z P, et al. Experimental observation of quantum contextuality beyond Bell nonlocality. Physical Review A, 2019, 100: 042118. doi: 10.1103/PhysRevA.100.042118
    [40]
    Xiao Y, Xu Z P, Li Q, et al. Experimental test of quantum correlations from platonic graphs. Optica, 2018, 5: 718–722. doi: 10.1364/OPTICA.5.000718
    [41]
    Klyachko A A, Can M A, Binicioglu S, et al. Simple test for hidden variables in spin-1 systems. Physical Review Letters, 2008, 101: 020403. doi: 10.1103/PhysRevLett.101.020403
    [42]
    Lapkiewicz R, Li P, Schaeff C, et al. Experimental non-classicality of an indivisible quantum system. Nature, 2011, 474: 490–493. doi: 10.1038/nature10119
    [43]
    Ahrens J, Amselem E, Cabello A, et al. Two fundamental experimental tests of nonclassicality with qutrits. Scientific Reports, 2013, 3: 2170. doi: https://doi.org/10.1038/srep02170
    [44]
    Jerger M, Reshitnyk Y, Oppliger M, et al. Contextuality without nonlocality in a superconducting quantum system. Nature Communications, 2016, 7: 12930. doi: 10.1038/ncomms12930
    [45]
    Simon C, Żukowski M, Weinfurter H, et al. Feasible “Kochen-Specker” experiment with single particles. Physical Review Letters, 2000, 85: 1783–1786. doi: 10.1103/PhysRevLett.85.1783
    [46]
    Amselem E, Bourennane M, Budroni C, et al. Comment on “state-independent experimental test of quantum contextuality in an indivisible system”. Physical Review Letters, 2013, 110: 078901. doi: 10.1103/PhysRevLett.110.078901
    [47]
    Huang Y F, Li M, Cao D Y, et al. Experimental test of state-independent quantum contextuality of an indivisible quantum system. Physical Review A, 2013, 87: 052133. doi: 10.1103/PhysRevA.87.052133
    [48]
    Cabello A, Amselem E, Blanchfield K, et al. Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality. Physical Review A, 2012, 85: 032108. doi: 10.1103/PhysRevA.85.032108
    [49]
    Broome M A, Fedrizzi A, Lanyon B P, et al. Discrete single-photon quantum walks with tunable decoherence. Physical Review Letters, 2010, 104: 153602. doi: 10.1103/PhysRevLett.104.153602
    [50]
    Mermin N D. Hidden variables and the two theorems of John Bell. Reviews of Modern Physics, 1993, 65: 803–815. doi: 10.1103/RevModPhys.65.803
    [51]
    Amselem E, Radmark M, Bourennane M, et al. State-independent quantum contextuality with single photons. Physical Review Letters, 2009, 103: 160405. doi: 10.1103/PhysRevLett.103.160405
    [52]
    Wang J, Zhou Y, Wang Z, et al. Bright room temperature single photon source at telecom range in cubic silicon carbide. Nature Communications, 2018, 9: 4106. doi: 10.1038/s41467-018-06605-3
    [53]
    Zhang A, Xu H, Xie J, et al. Experimental test of contextuality in quantum and classical systems. Physical Review Letters, 2019, 122: 080401. doi: 10.1103/PhysRevLett.122.080401
    [54]
    Qu D, Wang K, Xiao L, et al. State-independent test of quantum contextuality with either single photons or coherent light. npj Quantum Information, 2021, 7: 1. doi: 10.1038/s41534-020-00339-1
    [55]
    Allen L, Beijersbergen M W, Spreeuw R, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Physical Review A, 1992, 45: 8185–8189. doi: 10.1103/PhysRevA.45.8185
    [56]
    Bolduc E, Bent N, Santamato E, et al. Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram. Optics Letters, 2013, 38: 3546–3549. doi: 10.1364/OL.38.003546
    [57]
    Mair A, Vaziri A, Weihs G, et al. Entanglement of the orbital angular momentum states of photons. Nature, 2001, 412: 313–316. doi: 10.1038/35085529
    [58]
    Bent N, Qassim H, Tahir A, et al. Experimental realization of quantum tomography of photonic qudits via symmetric informationally complete positive operatorvalued measures. Physical Review X, 2015, 5: 041006. doi: 10.1103/PhysRevX.5.041006
    [59]
    Liu Z D, Sun Y N, Cheng Z D, et al. Experimental test of single-system steering and application to quantum communication. Physical Review A, 2017, 95: 022341. doi: 10.1103/PhysRevA.95.022341
    [60]
    Sun Y N, Liu Z D, Bowles J, et al. Experimental certification of quantum dimensions and irreducible high-dimensional quantum systems with independent devices. Optica, 2020, 7: 1073. doi: 10.1364/OPTICA.396932
    [61]
    Yang M, Xiao Y, Liao Y W, et al. Zonal reconstruction of photonic wavefunction via momentum weak measurement. Laser & Photonics Reviews, 2020, 14 (5): 1900251. doi: 10.1002/lpor.201900251
    [62]
    Zheng Y, Yang M, Liu Z H, et al. Detecting momentum weak value: Shack-Hartmann versus a weak measurement wavefront sensor. Optics Letters, 2021, 46: 5352. doi: 10.1364/OL.439174
    [63]
    Hao Z Y, Sun K, Wang Y, et al. Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering. Physical Review Letters, 2022, 128: 120402. doi: 10.1103/PhysRevLett.128.120402
    [64]
    Ru S, Tang W, Wang Y, et al. Verification of Kochen-Specker-type quantum contextuality with a single photon. Physical Review A, 2022, 105: 012428. doi: 10.1103/PhysRevA.105.012428
    [65]
    Wang X L, Luo Y H, Huang H L, et al. 18-qubit entanglement with six photons’ three degrees of freedom. Physical Review Letters, 2018, 120: 260502. doi: 10.1103/PhysRevLett.120.260502
    [66]
    Ru S, Wang Y, An M, et al. Realization of a deterministic quantum Toffoli gate with a single photon. Physical Review A, 2021, 103: 022606. doi: 10.1103/PhysRevA.103.022606
    [67]
    Greenberger D M, Horne M A, Shimony A, et al. Bell’s theorem without inequalities. American Journal of Physics, 1990, 58: 1131–1143. doi: 10.1119/1.16243
    [68]
    Brassard G, Broadbent A, Tapp A. Multi-party pseudo-telepathy. In: Dehne F, Sack J R, Smid M, editors. Algorithms and Data Structures (WADS 2003). Berlin, Germany: Springer, 2003: 1–11.
    [69]
    Abramsky S, Brandenburger A. The sheaf-theoretic structure of nonlocality and contextuality. New Journal of Physics, 2011, 13: 113036. doi: 10.1088/1367-2630/13/11/113036
    [70]
    Liu Z H, Zhou J, Meng H X, et al. Experimental test of the Greenberger-Horne-Zeilinger-type paradoxes in and beyond graph states. npj Quantum Information, 2021, 7: 66. doi: 10.1038/s41534-021-00397-z
    [71]
    Cabello A. “All versus nothing” inseparability for two observers. Physical Review Letters, 2001, 87: 010403. doi: 10.1103/PhysRevLett.87.010403
    [72]
    Bennett C H, Brassard G, Crépeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical Review Letters, 1993, 70: 1895–1899. doi: 10.1103/PhysRevLett.70.1895
    [73]
    Kwiat P G, Mattle K, Weinfurter H, et al. New high-intensity source of polarization-entangled photon pairs. Physical Review Letters, 1995, 75: 4337–4341. doi: 10.1103/PhysRevLett.75.4337
    [74]
    Chen Z B, Pan J W, Zhang Y D, et al. All-versus-nothing violation of local realism for two entangled photons. Physical Review Letters, 2003, 90: 160408. doi: 10.1103/PhysRevLett.90.160408
    [75]
    Yang T, Zhang Q, Zhang J, et al. All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement. Physical Review Letters, 2005, 95: 240406. doi: 10.1103/PhysRevLett.95.240406
    [76]
    Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2002.
    [77]
    Massar S, Pironio S, Roland J, et al. Bell inequalities resistant to detector inefficiency. Physical Review A, 2002, 66: 052112. doi: 10.1103/PhysRevA.66.052112
    [78]
    Wang P, Zhang J, Luan C Y, et al. Significant loophole-free test of Kochen-Specker contextuality using two species of atomic ions. Science Advances, 2022, 8: eabk1660. doi: 10.1126/sciadv.abk1660
    [79]
    Shalm L K, Meyer-Scott E, Christensen B G, et al. Strong loophole-free test of local realism. Physical Review Letters, 2015, 115: 250402. doi: 10.1103/PhysRevLett.115.250402
    [80]
    Giustina M, Versteegh M A,Wengerowsky S, et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Physical Review Letters, 2015, 115: 250401. doi: 10.1103/PhysRevLett.115.250401
    [81]
    Meyer D A. Finite precision measurement nullifies the Kochen-Specker theorem. Physical Review Letters, 1999, 83: 3751–3754. doi: 10.1103/PhysRevLett.83.3751
    [82]
    Kent A. Noncontextual hidden variables and physical measurements. Physical Review Letters, 1999, 83: 3755–3757. doi: 10.1103/PhysRevLett.83.3755
    [83]
    Kirchmair G, Zahringer F, Gerritsma R, et al. State-independent experimental test of quantum contextuality. Nature, 2009, 460: 494–497. doi: 10.1038/nature08172
    [84]
    Gühne O, Kleinmann M, Cabello A, et al. Compatibility and noncontextuality for sequential measurements. Physical Review A, 2010, 81: 022121. doi: 10.1103/PhysRevA.81.022121
    [85]
    Szangolies J, Kleinmann M, Gühne O. Tests against noncontextual models with measurement disturbances. Physical Review A, 2013, 87: 050101. doi: 10.1103/PhysRevA.87.050101
    [86]
    Cabello A, Cunha M T. Proposal of a two-qutrit contextuality test free of the finite precision and compatibility loopholes. Physical Review Letters, 2011, 106: 190401. doi: 10.1103/PhysRevLett.106.190401
    [87]
    Hu X M, Chen J S, Liu B H, et al. Experimental test of compatibility-loophole-free contextuality with spatially separated entangled qutrits. Physical Review Letters, 2016, 117: 170403. doi: 10.1103/PhysRevLett.117.170403
    [88]
    Hu X M, Xing W B, Liu B H, et al. Efficient generation of high-dimensional entanglement through multipath down-conversion. Physical Review Letters, 2020, 125: 090503. doi: 10.1103/PhysRevLett.125.090503
    [89]
    Li L, Liu Z, Ren X, et al. Metalens-array-based high-dimensional and multiphoton quantum source. Science, 2020, 368: 1487–1490. doi: 10.1126/science.aba9779
    [90]
    Svozil K. Staging quantum cryptography with chocolate balls. American Journal of Physics, 2006, 74: 800–803. doi: 10.1119/1.2205879
    [91]
    Cabello A, D’Ambrosio V, Nagali E, et al. Hybrid ququart-encoded quantum cryptography protected by Kochen-Specker contextuality. Physical Review A, 2011, 84: 030302. doi: 10.1103/PhysRevA.84.030302
    [92]
    Spekkens R W, Buzacott D H, Keehn A J, et al. Preparation contextuality powers parity-oblivious multiplexing. Physical Review Letters, 2009, 102: 010401. doi: 10.1103/PhysRevLett.102.010401
    [93]
    Saha D, Horodecki P, Pawlowski M. State independent contextuality advances one-way communication. New Journal of Physics, 2019, 21 (9): 093057. doi: 10.1088/1367-2630/ab4149
    [94]
    Abbott A A, Calude C S, Conder J, et al. Strong Kochen-Specker theorem and incomputability of quantum randomness. Physical Review A, 2012, 86: 062109. doi: 10.1103/PhysRevA.86.062109
    [95]
    Um M, Zhao Q, Zhang J, et al. Randomness expansion secured by quantum contextuality. Physical Review Applied, 2020, 13: 034077. doi: 10.1103/PhysRevApplied.13.034077
    [96]
    Bharti K, Ray M, Varvitsiotis A, et al. Robust self-testing of quantum systems via noncontextuality inequalities. Physical Review Letters, 2019, 122: 250403. doi: 10.1103/PhysRevLett.122.250403
    [97]
    Gühne O, Budroni C, Cabello A, et al. Bounding the quantum dimension with contextuality. Physical Review A, 2014, 89: 062107. doi: 10.1103/PhysRevA.89.062107
    [98]
    Ray M, Boddu N G, Bharti K, et al. Graph-theoretic approach to dimension witnessing. New Journal of Physics, 2021, 23: 033006. doi: 10.1088/1367-2630/abcacd
    [99]
    Preskill J. Quantum computing in the NISQ era and beyond. Quantum, 2018, 2: 79. doi: 10.22331/q-2018-08-06-79
    [100]
    Shor P W. Scheme for reducing decoherence in quantum computer memory. Physical Review A, 1995, 52: R2493. doi: 10.1103/PhysRevA.52.R2493
    [101]
    Nayak C, Simon S H, Stern A, et al. Non-Abelian anyons and topological quantum computation. Reviews of Modern Physics, 2008, 80: 1083. doi: 10.1103/RevModPhys.80.1083
    [102]
    Bravyi S, Kitaev A Y. Universal quantum computation with ideal Clifford gates and noisy ancillas. Physical Review A, 2005, 71: 022316. doi: 10.1103/PhysRevA.71.022316
    [103]
    Veitch V, Mousavian S H, Gottesman D, et al. The resource theory of stabilizer quantum computation. New Journal of Physics, 2014, 16: 013009. doi: 10.1088/1367-2630/16/1/013009
    [104]
    Kitaev A Y. Fault-tolerant quantum computation by anyons. Annals of Physics, 2003, 303: 2–30. doi: 10.1016/S0003-4916(02)00018-0
    [105]
    Bartolomei H, Kumar M, Bisognin R, et al. Fractional statistics in anyon collisions. Science, 2020, 368: 173–177. doi: 10.1126/science.aaz5601
    [106]
    Nakamura J, Liang S, Gardner G, et al. Direct observation of anyonic braiding statistics. Nature Physics, 2020, 16: 931–936. doi: 10.1038/s41567-020-1019-1
    [107]
    Liu Z H, Sun K, Pachos J K, et al. Topological contextuality and anyonic statistics of photonic-encoded parafermions. PRX Quantum, 2021, 2: 030323. doi: 10.1103/PRXQuantum.2.030323
    [108]
    Aspuru-Guzik A, Walther P. Photonic quantum simulators. Nature Physics, 2012, 8: 285–291. doi: 10.1038/nphys2253
    [109]
    Georgescu I M, Ashhab S, Nori F. Quantum simulation. Reviews of Modern Physics, 2014, 86: 153–185. doi: 10.1103/RevModPhys.86.153
    [110]
    Fradkin E, Kadanoff L P. Disorder variables and para-fermions in two-dimensional statistical mechanics. Nuclear Physics B, 1980, 170: 1. doi: 10.1016/0550-3213(80)90472-1
    [111]
    Bargmann V. Note on Wigner’s theorem on symmetry operations. Journal of Mathematical Physics, 1964, 5: 862. doi: 10.1063/1.1704188
    [112]
    Xu J S, Sun K, Han Y J, et al. Simulating the exchange of Majorana zero modes with a photonic system. Nature Communications, 2016, 7: 13194. doi: 10.1038/ncomms13194
    [113]
    Tang J S, Wang Y T, Yu S, et al. Experimental investigation of the no-signalling principle in parity-time symmetric theory using an open quantum system. Nature Photonics, 2016, 10: 642–646. doi: 10.1038/nphoton.2016.144
    [114]
    Wang Y T, Li Z P, Yu S, et al. Experimental investigation of state distinguishability in parity-time symmetric quantum dynamics. Physical Review Letters, 2020, 124: 230402. doi: 10.1103/PhysRevLett.124.230402
    [115]
    Yu S, Meng Y, Tang J S, et al. Experimental investigation of quantum PT-enhanced sensor. Physical Review Letters, 2020, 125: 240506. doi: 10.1103/PhysRevLett.125.240506
    [116]
    Li Q, Zhang C J, Cheng Z D, et al. Experimental simulation of anti-parity-time symmetric lorentz dynamics. Optica, 2019, 6: 67–71. doi: 10.1364/OPTICA.6.000067
    [117]
    Xu J S, Yung M H, Xu X Y, et al. Demon-like algorithmic quantum cooling and its realization with quantum optics. Nature Photonics, 2014, 8: 113–118. doi: 10.1038/nphoton.2013.354
    [118]
    Chuang I L, Nielsen M A. Prescription for experimental determination of the dynamics of a quantum black box. Journal of Modern Optics, 1997, 44: 2455–2467. doi: 10.1080/09500349708231894
    [119]
    O’Brien J L, Pryde G, Gilchrist A, et al. Quantum process tomography of a controlled-not gate. Physical Review Letters, 2004, 93: 080502. doi: 10.1103/PhysRevLett.93.080502
    [120]
    Cabello A. Bell non-locality and Kochen-Specker contextuality: How are they connected? Foundations of Physics, 2021, 51: 1. doi: 10.1007/s10701-021-00404-5
    [121]
    Cabello A. Converting contextuality into nonlocality. Physical Review Letters, 2021, 127: 070401. doi: 10.1103/PhysRevLett.127.070401
    [122]
    Clauser J F, Horne M A, Shimony A, et al. Proposed experiment to test local hidden-variable theories. Physical Review Letters, 1969, 23: 880–884. doi: 10.1103/PhysRevLett.23.880
    [123]
    Kurzyński P, Cabello A, Kaszlikowski D. Fundamental monogamy relation between contextuality and nonlocality. Physical Review Letters, 2014, 112: 100401. doi: 10.1103/PhysRevLett.112.100401
    [124]
    Zhan X, Zhang X, Li J, et al. Realization of the contextuality-nonlocality tradeoff with a qubit-qutrit photon pair. Physical Review Letters, 2016, 116: 090401. doi: 10.1103/PhysRevLett.116.090401
    [125]
    Cabello A. Proposal for revealing quantum nonlocality via local contextuality. Physical Review Letters, 2010, 104: 220401. doi: 10.1103/PhysRevLett.104.220401
    [126]
    Liu B H, Hu X M, Chen J S, et al. Nonlocality from local contextuality. Physical Review Letters, 2016, 117: 220402. doi: 10.1103/PhysRevLett.117.220402
    [127]
    Hu X M, Liu B H, Chen J S, et al. Simultaneous observation of quantum contextuality and quantum nonlocality. Science Bulletin, 2018, 63: 1092–1095. doi: 10.1016/j.scib.2018.06.018
    [128]
    Amselem E, Danielsen L E, Lopez-Tarrida A J, et al. Experimental fully contextual correlations. Physical Review Letters, 2012, 108: 200405. doi: 10.1103/PhysRevLett.108.200405
    [129]
    D’Ambrosio V, Herbauts I, Amselem E, et al. Experimental implementation of a Kochen-Specker set of quantum tests. Physical Review X, 2013, 3: 011012. doi: 10.1103/PhysRevX.3.011012
    [130]
    Qu D, Kurzyński P, Kaszlikowski D, et al. Experimental entropic test of state-independent contextuality via single photons. Physical Review A, 2020, 101: 060101. doi: 10.1103/PhysRevA.101.060101
    [131]
    Frustaglia D, Baltanás J P, Velázquez-Ahumada M C, et al. Classical physics and the bounds of quantum correlations. Physical Review Letters, 2016, 116: 250404. doi: 10.1103/PhysRevLett.116.250404
    [132]
    Liu B, Huang Y, Gong Y, et al. Experimental demonstration of quantum contextuality with nonentangled photons. Physical Review A, 2009, 80: 044101. doi: 10.1103/PhysRevA.80.044101
    [133]
    Cabello A. Proposed test of macroscopic quantum contextuality. Physical Review A, 2010, 82: 032110. doi: 10.1103/PhysRevA.82.032110
    [134]
    Vidick T, Wehner S. Does ignorance of the whole imply ignorance of the parts? Large violations of noncontextuality in quantum theory. Physical Review Letters, 2011, 107: 030402. doi: 10.1103/PhysRevLett.107.030402
    [135]
    Amaral B, Cunha M T, Cabello A. Quantum theory allows for absolute maximal contextuality. Physical Review A, 2015, 92: 062125. doi: 10.1103/PhysRevA.92.062125
    [136]
    Mermin N D. Extreme quantum entanglement in a superposition of macroscopically distinct states. Physical Review Letters, 1990, 65: 1838. doi: 10.1103/PhysRevLett.65.1838
    [137]
    Ardehali M. Bell inequalities with a magnitude of violation that grows exponentially with the number of particles. Physical Review A, 1992, 46: 5375–5378. doi: 10.1103/PhysRevA.46.5375
    [138]
    Belinskiĭ A, Klyshko D N. Interference of light and Bell’s theorem. Physics-Uspekhi, 1993, 36: 653. doi: 10.1070/pu1993v036n08abeh002299
    [139]
    Cavalcanti E G. Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning. Physical Review X, 2018, 8: 021018. doi: 10.1103/PhysRevX.8.021018
    [140]
    Pearl J, Cavalcanti E. Classical causal models cannot faithfully explain Bell nonlocality or Kochen-Specker contextuality in arbitrary scenarios. Quantum, 2021, 5: 518. doi: 10.22331/q-2021-08-05-518
    [141]
    Hu X M, Xie Y, Arora A S, et al. Self-testing of a single quantum system: Theory and experiment. [2022-03-01]. https://arxiv.org/abs/2203.09003v1.
    [142]
    Xu J S, Sun K, Pachos J K, et al. Photonic implementation of Majorana-based Berry phases. Science Advances, 2018, 4: eaat6533. doi: 10.1126/sciadv.aat6533
    [143]
    Liu C, Huang H L, Chen C, et al. Demonstration of topologically path-independent anyonic braiding in a nine-qubit planar code. Optica, 2019, 6: 264–268. doi: 10.1364/OPTICA.6.000264
    [144]
    Huang H L, Narożniak M, Liang F, et al. Emulating quantum teleportation of a Majorana zero mode qubit. Physical Review Letters, 2021, 126: 090502. doi: 10.1103/PhysRevLett.126.090502
    [145]
    Kirby W M, Tranter A, Love P J. Contextual subspace variational quantum eigensolver. Quantum, 2021, 5: 456. doi: 10.22331/q-2021-05-14-456
    [146]
    Widmann M, Lee S Y, Rendler T, et al. Coherent control of single spins in silicon carbide at room temperature. Nature Materials, 2015, 14: 164–168. doi: 10.1038/nmat4145
    [147]
    Wang J F, Yan F F, Li Q, et al. Coherent control of nitrogen-vacancy center spins in silicon carbide at room temperature. Physical Review Letters, 2020, 124: 223601. doi: 10.1103/PhysRevLett.124.223601
    [148]
    Wang J F, Yan F F, Li Q, et al. Robust coherent control of solid-state spin qubits using anti-Stokes excitation. Nature Communications, 2021, 12: 3223. doi: 10.1038/s41467-021-23471-8
    [149]
    Xu Z P, Saha D, Su H Y, et al. Reformulating noncontextuality inequalities in an operational approach. Physical Review A, 2016, 94: 062103. doi: 10.1103/PhysRevA.94.062103
    [150]
    Leifer M, Duarte C. Noncontextuality inequalities from antidistinguishability. Physical Review A, 2020, 101: 062113. doi: 10.1103/PhysRevA.101.062113
    [151]
    Lovász L, Saks M, Schrijver A. Orthogonal representations and connectivity of graphs. Linear Algebra and Its Applications, 1989, 114: 439–454. doi: 10.1016/0024-3795(89)90475-8
  • 加载中

Catalog

    Figure  1.  The Yu-Oh 13-ray appearing in the state-independent proof of contextuality by Yu and Oh[21]. Left: the geometric representation of the rays in a unit cube. The rays are defined as $y^{-}_{1} =(0,1,-1),\; y_{2} ^{-} =(-1,0,1),\; y_{3} ^{-} =(1,-1,0),\; y_{1} ^{+} =(0,1,1),\; y_{2} ^{+} =(1,0,1),\; y_{3} ^{+} =(1,1,0),\; h_{0} =(1,1,1),\; h_{1} =(-1,1,1),\; h_{2} =(1,-1,1),\; $$ h_{3} =(1,1,-1),\; z_{1} =(1,0,0),\; z_{2} =(0,1,0),\; z_{3} =(0,0,1).$ Right: the orthogonality relationship among the set of rays. Each vertex represents a ray; when two vertices are linked by an edge, the corresponding rays are orthogonal. Figure taken from Ref. [21].

    Figure  2.  Contextuality from a Platonic graph. (a) A regular icosahedron is a Platonic solid with 12 vertices and 20 edges. (b) The icosahedron graph (vertices 1–12) is the skeleton of the icosahedron. With the auxiliary vertices 13–16 every vertex belongs to a 4-clique, and the graph’s complement graph has a Lovász orthogonal representation[151] in dimension 4. (c) The violation of the noncontextuality inequality dual to the icosahedron graph decreases with the linear entropy of a quantum state characterizing the mixedness of the state. Figure taken from Ref. [40].

    Figure  3.  First experimental test of contextuality at USTC. Main: experimental setup. A heralded single photon’s path and polarization degrees of freedom encode two qubits. The half-wave plates and polarizing beam splitters inside the two Mach-Zehnder interferometers conducted the first joint path-polarization measurement and that after the interferometers executed the second joint measurement. HWP half-wave plate and PBS polarizing beam splitter. Inset: Experimental result showing event probabilities in accord with the predictions of the noncontextual hidden-variable and quantum theories. Figure adapted from Ref. [23].

    Figure  4.  A “standard” experimental setup for testing noncontextuality inequalities containing up to two-point correlations with a photonic qutrit system. To extract the two-point correlation without prematurely destroying the photon, the measurement result of the first observable is registered in the path degree of freedom. The inset shows the experimental violation of the noncontextuality inequality (17) for seven pure states and the maximally mixed state. Figure adapted from Ref. [47].

    Figure  5.  Simplification of contextuality experiments. Top: implementing successive measurements poses the main technical challenge on photonic contextuality experiments. Middle: by adopting the graph-theoretical approach to contextuality, the required number of sequential measurements can be reduced to one. Bottom: by assuming the Lüders’ rule, the sequential measurement can be substituted by a destructive measurement and a repreparation procedure, thus completely lifting the requirement of sequential measurements from contextuality experiments at the price of some conceptual disadvantages. Figure taken from Ref. [36].

    Figure  6.  A photonic prepare-and-measure setup for testing graph-theoretic noncontextuality inequalities. (a)-(c) With the repreparation procedure, the two-point correlations can be calculated via Eq. (13) and Eq. (19). (d) Experimental results of the contextuality test. (e) Verification of the no-signaling condition. Figure taken from Ref. [38].

    Figure  7.  A high-dimensional photonic prepare-and-measure setup, where the quantum information was encoded on the orbital angular momentum degree of freedom.

    Figure  8.  Observation of an all-versus-nothing contextuality. (a) Experimental setup. By pumping a nonlinear crystal twice, the two photons received by the two observers became path-polarization hyperentangled. Different apparatuses were devised to measure different path observables. (b) Predictions by noncontextual hidden-variable theory (left) and quantum theory (right) on the probabilities of events in Eq. (23). (c) Experimental results and the quantum prediction are in accord. Figure taken from Ref. [75]

    Figure  9.  Experimental setup for observing a compatibility-loophole-free contextuality. Part A implemented state preparation, where maximally entangled qutrits were generated on the photonic path degrees of freedom. Part B implemented qutrit measurements, where the path states of the photons were analyzed. Figure taken from Ref. [87].

    Figure  10.  Behaviors of topological contextuality under braiding and local noise. (a) A Bloch sphere illustrating the effect of $ \mathbb{Z}_3 $-parafermion braiding on the encoded qutrit. A geometric phase of $ 2\pi/3 $ is obtained between one and the other two computational bases. (b) The real parts of the theoretical (edge) and experimental (filling) braiding process matrices. (c) Permutation of the magic contextuality witnesses. (d) The violations of magic noncontextuality inequality (32) were almost invariant for the sample states. (e) The real parts of the theoretical (edge) and experimental (filling) local noise process matrices. (f) The dynamics of magic contextuality under hopping noise for a topologically-protected qutrit (blue) and under flip noise for a trivial (not protected) qutrit (orange). Figure adapted from Ref. [107].

    Figure  11.  Setup for observation of nonlocality activated by local contextuality. (a) Schematic illustration of the experiment. Alice and Bob share two pairs of Bell states. Alice implements a contextuality test on her qubits and checks the correlations of her observables with Bob’s. (b) Devices for measuring the nine observables in the contextuality test. (c) Experimental result demonstrating the activation of nonlocality from local contextuality. Figure adapted from Ref. [126].

    [1]
    Shor P W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Review, 1999, 41: 303–332. doi: 10.1137/S0036144598347011
    [2]
    Zhong H S, Wang H, Deng Y H, et al. Quantum computational advantage using photons. Science, 2020, 370: 1460–1463. doi: 10.1126/science.abe8770
    [3]
    Arrazola J, Bergholm V, Brádler K, et al. Quantum circuits with many photons on a programmable nanophotonic chip. Nature, 2021, 591: 54–60. doi: 10.1038/s41586-021-03202-1
    [4]
    Zhong H S, Deng Y H, Qin J, et al. Phase-programmable Gaussian boson sampling using stimulated squeezed light. Physical Review Letters, 2021, 127: 180502. doi: 10.1103/PhysRevLett.127.180502
    [5]
    Aaronson S, Arkhipov A. The computational complexity of linear optics. In: STOC ’11: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing. San Jose, USA: Association for Computing Machinery, 2011: 333–342.
    [6]
    Hamilton C S, Kruse R, Sansoni L, et al. Gaussian boson sampling. Physical Review Letters, 2017, 119: 170501. doi: 10.1103/PhysRevLett.119.170501
    [7]
    Gottesman D. The Heisenberg representation of quantum computers. [2022-03-01]. https://arxiv.org/abs/quant-ph/9807006.
    [8]
    Braunstein S L, van Loock P. Quantum information with continuous variables. Reviews of Modern Physics, 2005, 77: 513–577. doi: 10.1103/RevModPhys.77.513
    [9]
    Greenberger D M, Horne M A, Zeilinger A. Going beyond Bell’s theorem. In: Kafatos M editor. Bell’s Theorem, Quantum Theory and Conceptions of the Universe. AG, Switzerland: Springer, 1989: 69–72.
    [10]
    Hardy L. Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. Physical Review Letters, 1992, 68: 2981–2984. doi: 10.1103/PhysRevLett.68.2981
    [11]
    Leifer M S, Spekkens R W. Pre-and post-selection paradoxes and contextuality in quantum mechanics. Physical Review Letters, 2005, 95: 200405. doi: 10.1103/PhysRevLett.95.200405
    [12]
    Yu S, Oh C H, Quantum pigeonhole effect, Cheshire cat and contextuality. [2022-03-01]. https://arxiv.org/abs/1408.2477.
    [13]
    Abramsky S, Barbosa R S, Kishida K,et al. Contextuality, cohomology and paradox. In: Kreutzer S, editor. 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Dagstuhl, Germany: Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2015: 211–228.
    [14]
    Waegell M, Tollaksen J. Contextuality, pigeonholes, Cheshire cats, mean kings, and weak values. Quantum Studies: Mathematics and Foundations, 2018, 5: 325–349. doi: 10.1007/s40509-017-0127-9
    [15]
    Liu Z H, Pan W W, Xu X Y, et al. Experimental exchange of grins between quantum Cheshire cats. Nature Communications, 2020, 11: 3006. doi: 10.1038/s41467-020-16761-0
    [16]
    Howard M, Wallman J, Veitch V, et al. Contextuality supplies the “magic” for quantum computation. Nature, 2014, 510: 351–355. doi: 10.1038/nature13460
    [17]
    Spekkens R W. Negativity and contextuality are equivalent notions of nonclassicality. Physical Review Letters, 2008, 101: 020401. doi: 10.1103/PhysRevLett.101.020401
    [18]
    Raussendorf R. Contextuality in measurement-based quantum computation. Physical Review A, 2013, 88: 022322. doi: 10.1103/PhysRevA.88.022322
    [19]
    Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete? Physical Review, 1935, 47: 777–780. doi: 10.1103/PhysRev.47.777
    [20]
    Kochen S, Specker S. The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics, 1967, 17: 59–87.
    [21]
    Yu S, Oh C H. State-independent proof of Kochen-Specker theorem with 13 rays. Physical Review Letters, 2012, 108: 030402. doi: 10.1103/PhysRevLett.108.030402
    [22]
    Cabello A, Kleinmann M, Portillo J R. Quantum state-independent contextuality requires 13 rays. Journal of Physics A: Mathematical and Theoretical, 2016, 49: 38LT01. doi: 10.1088/1751-8113/49/38/38LT01
    [23]
    Huang Y F, Li C F, Zhang Y S, et al. Experimental test of the Kochen-Specker theorem with single photons. Physical Review Letters, 2003, 90: 250401. doi: 10.1103/PhysRevLett.90.250401
    [24]
    Flamini F, Spagnolo N, Sciarrino F. Photonic quantum information processing: A review. Reports on Progress in Physics, 2018, 82 (1): 016001. doi: 10.1088/1361-6633/aad5b2
    [25]
    Budroni C, Cabello A, Gühne O, et al. Quantum contextuality. [2022-03-15]. https://doi.org/10.48550/arXiv.2102.13036.
    [26]
    Thompson J, Kurzyński P, Lee S Y, et al. Recent advances in contextuality tests. Open Systems & Information Dynamics, 2016, 23: 1650009. doi: 10.1142/S1230161216500098
    [27]
    Cabello A, Severini S, Winter A. Graph-theoretic approach to quantum correlations. Physical Review Letters, 2014, 112: 040401. doi: 10.1103/PhysRevLett.112.040401
    [28]
    Xu Z P, Yu X D, Kleinmann M. State-independent quantum contextuality with projectors of nonunit rank. New Journal of Physics, 2021, 23: 043025. doi: 10.1088/1367-2630/abe6e3
    [29]
    Fine A. Hidden variables, joint probability, and the Bell inequalities. Physical Review Letters, 1982, 48: 291. doi: 10.1103/PhysRevLett.48.291
    [30]
    Cabello A, Estebaranz J M, García-Alcaine G. Bell-Kochen-Specker theorem: A proof with 18 vectors. Physics Letters A, 1996, 212: 183–187. doi: 10.1016/0375-9601(96)00134-X
    [31]
    Xu Z P, Chen J L, Gühne O. Proof of the Peres conjecture for contextuality. Physical Review Letters, 2020, 124: 230401. doi: 10.1103/PhysRevLett.124.230401
    [32]
    Uijlen S, Westerbaan B. A Kochen-Specker system has at least 22 vectors. New Generation Computing, 2016, 34: 3–23. doi: 10.1007/s00354-016-0202-5
    [33]
    Peres A. Two simple proofs of the Kochen-Specker theorem. Journal of Physics A: Mathematical and General, 1991, 24: L175. doi: 10.1088/0305-4470/24/4/003
    [34]
    Cabello A. Experimentally testable state-independent quantum contextuality. Physical Review Letters, 2008, 101: 210401. doi: 10.1103/PhysRevLett.101.210401
    [35]
    Lovász L. On the Shannon capacity of a graph. IEEE Transactions on Information Theory, 1979, 25: 1–7. doi: 10.1109/TIT.1979.1055985
    [36]
    Cabello A. Simple method for experimentally testing any form of quantum contextuality. Physical Review A, 2016, 93: 032102. doi: 10.1103/PhysRevA.93.032102
    [37]
    Cañas G, Acuña E, Cariñe J, et al. Experimental demonstration of the connection between quantum contextuality and graph theory. Physical Review A, 2016, 94: 012337. doi: 10.1103/PhysRevA.94.012337
    [38]
    Xiao Y, Xu Z P, Li Q, et al. Experimental observation of quantum state-independent contextuality under no-signaling conditions. Optics Express, 2018, 26: 32. doi: 10.1364/OE.26.000032
    [39]
    Liu Z H, Meng H X, Xu Z P, et al. Experimental observation of quantum contextuality beyond Bell nonlocality. Physical Review A, 2019, 100: 042118. doi: 10.1103/PhysRevA.100.042118
    [40]
    Xiao Y, Xu Z P, Li Q, et al. Experimental test of quantum correlations from platonic graphs. Optica, 2018, 5: 718–722. doi: 10.1364/OPTICA.5.000718
    [41]
    Klyachko A A, Can M A, Binicioglu S, et al. Simple test for hidden variables in spin-1 systems. Physical Review Letters, 2008, 101: 020403. doi: 10.1103/PhysRevLett.101.020403
    [42]
    Lapkiewicz R, Li P, Schaeff C, et al. Experimental non-classicality of an indivisible quantum system. Nature, 2011, 474: 490–493. doi: 10.1038/nature10119
    [43]
    Ahrens J, Amselem E, Cabello A, et al. Two fundamental experimental tests of nonclassicality with qutrits. Scientific Reports, 2013, 3: 2170. doi: https://doi.org/10.1038/srep02170
    [44]
    Jerger M, Reshitnyk Y, Oppliger M, et al. Contextuality without nonlocality in a superconducting quantum system. Nature Communications, 2016, 7: 12930. doi: 10.1038/ncomms12930
    [45]
    Simon C, Żukowski M, Weinfurter H, et al. Feasible “Kochen-Specker” experiment with single particles. Physical Review Letters, 2000, 85: 1783–1786. doi: 10.1103/PhysRevLett.85.1783
    [46]
    Amselem E, Bourennane M, Budroni C, et al. Comment on “state-independent experimental test of quantum contextuality in an indivisible system”. Physical Review Letters, 2013, 110: 078901. doi: 10.1103/PhysRevLett.110.078901
    [47]
    Huang Y F, Li M, Cao D Y, et al. Experimental test of state-independent quantum contextuality of an indivisible quantum system. Physical Review A, 2013, 87: 052133. doi: 10.1103/PhysRevA.87.052133
    [48]
    Cabello A, Amselem E, Blanchfield K, et al. Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality. Physical Review A, 2012, 85: 032108. doi: 10.1103/PhysRevA.85.032108
    [49]
    Broome M A, Fedrizzi A, Lanyon B P, et al. Discrete single-photon quantum walks with tunable decoherence. Physical Review Letters, 2010, 104: 153602. doi: 10.1103/PhysRevLett.104.153602
    [50]
    Mermin N D. Hidden variables and the two theorems of John Bell. Reviews of Modern Physics, 1993, 65: 803–815. doi: 10.1103/RevModPhys.65.803
    [51]
    Amselem E, Radmark M, Bourennane M, et al. State-independent quantum contextuality with single photons. Physical Review Letters, 2009, 103: 160405. doi: 10.1103/PhysRevLett.103.160405
    [52]
    Wang J, Zhou Y, Wang Z, et al. Bright room temperature single photon source at telecom range in cubic silicon carbide. Nature Communications, 2018, 9: 4106. doi: 10.1038/s41467-018-06605-3
    [53]
    Zhang A, Xu H, Xie J, et al. Experimental test of contextuality in quantum and classical systems. Physical Review Letters, 2019, 122: 080401. doi: 10.1103/PhysRevLett.122.080401
    [54]
    Qu D, Wang K, Xiao L, et al. State-independent test of quantum contextuality with either single photons or coherent light. npj Quantum Information, 2021, 7: 1. doi: 10.1038/s41534-020-00339-1
    [55]
    Allen L, Beijersbergen M W, Spreeuw R, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Physical Review A, 1992, 45: 8185–8189. doi: 10.1103/PhysRevA.45.8185
    [56]
    Bolduc E, Bent N, Santamato E, et al. Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram. Optics Letters, 2013, 38: 3546–3549. doi: 10.1364/OL.38.003546
    [57]
    Mair A, Vaziri A, Weihs G, et al. Entanglement of the orbital angular momentum states of photons. Nature, 2001, 412: 313–316. doi: 10.1038/35085529
    [58]
    Bent N, Qassim H, Tahir A, et al. Experimental realization of quantum tomography of photonic qudits via symmetric informationally complete positive operatorvalued measures. Physical Review X, 2015, 5: 041006. doi: 10.1103/PhysRevX.5.041006
    [59]
    Liu Z D, Sun Y N, Cheng Z D, et al. Experimental test of single-system steering and application to quantum communication. Physical Review A, 2017, 95: 022341. doi: 10.1103/PhysRevA.95.022341
    [60]
    Sun Y N, Liu Z D, Bowles J, et al. Experimental certification of quantum dimensions and irreducible high-dimensional quantum systems with independent devices. Optica, 2020, 7: 1073. doi: 10.1364/OPTICA.396932
    [61]
    Yang M, Xiao Y, Liao Y W, et al. Zonal reconstruction of photonic wavefunction via momentum weak measurement. Laser & Photonics Reviews, 2020, 14 (5): 1900251. doi: 10.1002/lpor.201900251
    [62]
    Zheng Y, Yang M, Liu Z H, et al. Detecting momentum weak value: Shack-Hartmann versus a weak measurement wavefront sensor. Optics Letters, 2021, 46: 5352. doi: 10.1364/OL.439174
    [63]
    Hao Z Y, Sun K, Wang Y, et al. Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering. Physical Review Letters, 2022, 128: 120402. doi: 10.1103/PhysRevLett.128.120402
    [64]
    Ru S, Tang W, Wang Y, et al. Verification of Kochen-Specker-type quantum contextuality with a single photon. Physical Review A, 2022, 105: 012428. doi: 10.1103/PhysRevA.105.012428
    [65]
    Wang X L, Luo Y H, Huang H L, et al. 18-qubit entanglement with six photons’ three degrees of freedom. Physical Review Letters, 2018, 120: 260502. doi: 10.1103/PhysRevLett.120.260502
    [66]
    Ru S, Wang Y, An M, et al. Realization of a deterministic quantum Toffoli gate with a single photon. Physical Review A, 2021, 103: 022606. doi: 10.1103/PhysRevA.103.022606
    [67]
    Greenberger D M, Horne M A, Shimony A, et al. Bell’s theorem without inequalities. American Journal of Physics, 1990, 58: 1131–1143. doi: 10.1119/1.16243
    [68]
    Brassard G, Broadbent A, Tapp A. Multi-party pseudo-telepathy. In: Dehne F, Sack J R, Smid M, editors. Algorithms and Data Structures (WADS 2003). Berlin, Germany: Springer, 2003: 1–11.
    [69]
    Abramsky S, Brandenburger A. The sheaf-theoretic structure of nonlocality and contextuality. New Journal of Physics, 2011, 13: 113036. doi: 10.1088/1367-2630/13/11/113036
    [70]
    Liu Z H, Zhou J, Meng H X, et al. Experimental test of the Greenberger-Horne-Zeilinger-type paradoxes in and beyond graph states. npj Quantum Information, 2021, 7: 66. doi: 10.1038/s41534-021-00397-z
    [71]
    Cabello A. “All versus nothing” inseparability for two observers. Physical Review Letters, 2001, 87: 010403. doi: 10.1103/PhysRevLett.87.010403
    [72]
    Bennett C H, Brassard G, Crépeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical Review Letters, 1993, 70: 1895–1899. doi: 10.1103/PhysRevLett.70.1895
    [73]
    Kwiat P G, Mattle K, Weinfurter H, et al. New high-intensity source of polarization-entangled photon pairs. Physical Review Letters, 1995, 75: 4337–4341. doi: 10.1103/PhysRevLett.75.4337
    [74]
    Chen Z B, Pan J W, Zhang Y D, et al. All-versus-nothing violation of local realism for two entangled photons. Physical Review Letters, 2003, 90: 160408. doi: 10.1103/PhysRevLett.90.160408
    [75]
    Yang T, Zhang Q, Zhang J, et al. All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement. Physical Review Letters, 2005, 95: 240406. doi: 10.1103/PhysRevLett.95.240406
    [76]
    Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2002.
    [77]
    Massar S, Pironio S, Roland J, et al. Bell inequalities resistant to detector inefficiency. Physical Review A, 2002, 66: 052112. doi: 10.1103/PhysRevA.66.052112
    [78]
    Wang P, Zhang J, Luan C Y, et al. Significant loophole-free test of Kochen-Specker contextuality using two species of atomic ions. Science Advances, 2022, 8: eabk1660. doi: 10.1126/sciadv.abk1660
    [79]
    Shalm L K, Meyer-Scott E, Christensen B G, et al. Strong loophole-free test of local realism. Physical Review Letters, 2015, 115: 250402. doi: 10.1103/PhysRevLett.115.250402
    [80]
    Giustina M, Versteegh M A,Wengerowsky S, et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Physical Review Letters, 2015, 115: 250401. doi: 10.1103/PhysRevLett.115.250401
    [81]
    Meyer D A. Finite precision measurement nullifies the Kochen-Specker theorem. Physical Review Letters, 1999, 83: 3751–3754. doi: 10.1103/PhysRevLett.83.3751
    [82]
    Kent A. Noncontextual hidden variables and physical measurements. Physical Review Letters, 1999, 83: 3755–3757. doi: 10.1103/PhysRevLett.83.3755
    [83]
    Kirchmair G, Zahringer F, Gerritsma R, et al. State-independent experimental test of quantum contextuality. Nature, 2009, 460: 494–497. doi: 10.1038/nature08172
    [84]
    Gühne O, Kleinmann M, Cabello A, et al. Compatibility and noncontextuality for sequential measurements. Physical Review A, 2010, 81: 022121. doi: 10.1103/PhysRevA.81.022121
    [85]
    Szangolies J, Kleinmann M, Gühne O. Tests against noncontextual models with measurement disturbances. Physical Review A, 2013, 87: 050101. doi: 10.1103/PhysRevA.87.050101
    [86]
    Cabello A, Cunha M T. Proposal of a two-qutrit contextuality test free of the finite precision and compatibility loopholes. Physical Review Letters, 2011, 106: 190401. doi: 10.1103/PhysRevLett.106.190401
    [87]
    Hu X M, Chen J S, Liu B H, et al. Experimental test of compatibility-loophole-free contextuality with spatially separated entangled qutrits. Physical Review Letters, 2016, 117: 170403. doi: 10.1103/PhysRevLett.117.170403
    [88]
    Hu X M, Xing W B, Liu B H, et al. Efficient generation of high-dimensional entanglement through multipath down-conversion. Physical Review Letters, 2020, 125: 090503. doi: 10.1103/PhysRevLett.125.090503
    [89]
    Li L, Liu Z, Ren X, et al. Metalens-array-based high-dimensional and multiphoton quantum source. Science, 2020, 368: 1487–1490. doi: 10.1126/science.aba9779
    [90]
    Svozil K. Staging quantum cryptography with chocolate balls. American Journal of Physics, 2006, 74: 800–803. doi: 10.1119/1.2205879
    [91]
    Cabello A, D’Ambrosio V, Nagali E, et al. Hybrid ququart-encoded quantum cryptography protected by Kochen-Specker contextuality. Physical Review A, 2011, 84: 030302. doi: 10.1103/PhysRevA.84.030302
    [92]
    Spekkens R W, Buzacott D H, Keehn A J, et al. Preparation contextuality powers parity-oblivious multiplexing. Physical Review Letters, 2009, 102: 010401. doi: 10.1103/PhysRevLett.102.010401
    [93]
    Saha D, Horodecki P, Pawlowski M. State independent contextuality advances one-way communication. New Journal of Physics, 2019, 21 (9): 093057. doi: 10.1088/1367-2630/ab4149
    [94]
    Abbott A A, Calude C S, Conder J, et al. Strong Kochen-Specker theorem and incomputability of quantum randomness. Physical Review A, 2012, 86: 062109. doi: 10.1103/PhysRevA.86.062109
    [95]
    Um M, Zhao Q, Zhang J, et al. Randomness expansion secured by quantum contextuality. Physical Review Applied, 2020, 13: 034077. doi: 10.1103/PhysRevApplied.13.034077
    [96]
    Bharti K, Ray M, Varvitsiotis A, et al. Robust self-testing of quantum systems via noncontextuality inequalities. Physical Review Letters, 2019, 122: 250403. doi: 10.1103/PhysRevLett.122.250403
    [97]
    Gühne O, Budroni C, Cabello A, et al. Bounding the quantum dimension with contextuality. Physical Review A, 2014, 89: 062107. doi: 10.1103/PhysRevA.89.062107
    [98]
    Ray M, Boddu N G, Bharti K, et al. Graph-theoretic approach to dimension witnessing. New Journal of Physics, 2021, 23: 033006. doi: 10.1088/1367-2630/abcacd
    [99]
    Preskill J. Quantum computing in the NISQ era and beyond. Quantum, 2018, 2: 79. doi: 10.22331/q-2018-08-06-79
    [100]
    Shor P W. Scheme for reducing decoherence in quantum computer memory. Physical Review A, 1995, 52: R2493. doi: 10.1103/PhysRevA.52.R2493
    [101]
    Nayak C, Simon S H, Stern A, et al. Non-Abelian anyons and topological quantum computation. Reviews of Modern Physics, 2008, 80: 1083. doi: 10.1103/RevModPhys.80.1083
    [102]
    Bravyi S, Kitaev A Y. Universal quantum computation with ideal Clifford gates and noisy ancillas. Physical Review A, 2005, 71: 022316. doi: 10.1103/PhysRevA.71.022316
    [103]
    Veitch V, Mousavian S H, Gottesman D, et al. The resource theory of stabilizer quantum computation. New Journal of Physics, 2014, 16: 013009. doi: 10.1088/1367-2630/16/1/013009
    [104]
    Kitaev A Y. Fault-tolerant quantum computation by anyons. Annals of Physics, 2003, 303: 2–30. doi: 10.1016/S0003-4916(02)00018-0
    [105]
    Bartolomei H, Kumar M, Bisognin R, et al. Fractional statistics in anyon collisions. Science, 2020, 368: 173–177. doi: 10.1126/science.aaz5601
    [106]
    Nakamura J, Liang S, Gardner G, et al. Direct observation of anyonic braiding statistics. Nature Physics, 2020, 16: 931–936. doi: 10.1038/s41567-020-1019-1
    [107]
    Liu Z H, Sun K, Pachos J K, et al. Topological contextuality and anyonic statistics of photonic-encoded parafermions. PRX Quantum, 2021, 2: 030323. doi: 10.1103/PRXQuantum.2.030323
    [108]
    Aspuru-Guzik A, Walther P. Photonic quantum simulators. Nature Physics, 2012, 8: 285–291. doi: 10.1038/nphys2253
    [109]
    Georgescu I M, Ashhab S, Nori F. Quantum simulation. Reviews of Modern Physics, 2014, 86: 153–185. doi: 10.1103/RevModPhys.86.153
    [110]
    Fradkin E, Kadanoff L P. Disorder variables and para-fermions in two-dimensional statistical mechanics. Nuclear Physics B, 1980, 170: 1. doi: 10.1016/0550-3213(80)90472-1
    [111]
    Bargmann V. Note on Wigner’s theorem on symmetry operations. Journal of Mathematical Physics, 1964, 5: 862. doi: 10.1063/1.1704188
    [112]
    Xu J S, Sun K, Han Y J, et al. Simulating the exchange of Majorana zero modes with a photonic system. Nature Communications, 2016, 7: 13194. doi: 10.1038/ncomms13194
    [113]
    Tang J S, Wang Y T, Yu S, et al. Experimental investigation of the no-signalling principle in parity-time symmetric theory using an open quantum system. Nature Photonics, 2016, 10: 642–646. doi: 10.1038/nphoton.2016.144
    [114]
    Wang Y T, Li Z P, Yu S, et al. Experimental investigation of state distinguishability in parity-time symmetric quantum dynamics. Physical Review Letters, 2020, 124: 230402. doi: 10.1103/PhysRevLett.124.230402
    [115]
    Yu S, Meng Y, Tang J S, et al. Experimental investigation of quantum PT-enhanced sensor. Physical Review Letters, 2020, 125: 240506. doi: 10.1103/PhysRevLett.125.240506
    [116]
    Li Q, Zhang C J, Cheng Z D, et al. Experimental simulation of anti-parity-time symmetric lorentz dynamics. Optica, 2019, 6: 67–71. doi: 10.1364/OPTICA.6.000067
    [117]
    Xu J S, Yung M H, Xu X Y, et al. Demon-like algorithmic quantum cooling and its realization with quantum optics. Nature Photonics, 2014, 8: 113–118. doi: 10.1038/nphoton.2013.354
    [118]
    Chuang I L, Nielsen M A. Prescription for experimental determination of the dynamics of a quantum black box. Journal of Modern Optics, 1997, 44: 2455–2467. doi: 10.1080/09500349708231894
    [119]
    O’Brien J L, Pryde G, Gilchrist A, et al. Quantum process tomography of a controlled-not gate. Physical Review Letters, 2004, 93: 080502. doi: 10.1103/PhysRevLett.93.080502
    [120]
    Cabello A. Bell non-locality and Kochen-Specker contextuality: How are they connected? Foundations of Physics, 2021, 51: 1. doi: 10.1007/s10701-021-00404-5
    [121]
    Cabello A. Converting contextuality into nonlocality. Physical Review Letters, 2021, 127: 070401. doi: 10.1103/PhysRevLett.127.070401
    [122]
    Clauser J F, Horne M A, Shimony A, et al. Proposed experiment to test local hidden-variable theories. Physical Review Letters, 1969, 23: 880–884. doi: 10.1103/PhysRevLett.23.880
    [123]
    Kurzyński P, Cabello A, Kaszlikowski D. Fundamental monogamy relation between contextuality and nonlocality. Physical Review Letters, 2014, 112: 100401. doi: 10.1103/PhysRevLett.112.100401
    [124]
    Zhan X, Zhang X, Li J, et al. Realization of the contextuality-nonlocality tradeoff with a qubit-qutrit photon pair. Physical Review Letters, 2016, 116: 090401. doi: 10.1103/PhysRevLett.116.090401
    [125]
    Cabello A. Proposal for revealing quantum nonlocality via local contextuality. Physical Review Letters, 2010, 104: 220401. doi: 10.1103/PhysRevLett.104.220401
    [126]
    Liu B H, Hu X M, Chen J S, et al. Nonlocality from local contextuality. Physical Review Letters, 2016, 117: 220402. doi: 10.1103/PhysRevLett.117.220402
    [127]
    Hu X M, Liu B H, Chen J S, et al. Simultaneous observation of quantum contextuality and quantum nonlocality. Science Bulletin, 2018, 63: 1092–1095. doi: 10.1016/j.scib.2018.06.018
    [128]
    Amselem E, Danielsen L E, Lopez-Tarrida A J, et al. Experimental fully contextual correlations. Physical Review Letters, 2012, 108: 200405. doi: 10.1103/PhysRevLett.108.200405
    [129]
    D’Ambrosio V, Herbauts I, Amselem E, et al. Experimental implementation of a Kochen-Specker set of quantum tests. Physical Review X, 2013, 3: 011012. doi: 10.1103/PhysRevX.3.011012
    [130]
    Qu D, Kurzyński P, Kaszlikowski D, et al. Experimental entropic test of state-independent contextuality via single photons. Physical Review A, 2020, 101: 060101. doi: 10.1103/PhysRevA.101.060101
    [131]
    Frustaglia D, Baltanás J P, Velázquez-Ahumada M C, et al. Classical physics and the bounds of quantum correlations. Physical Review Letters, 2016, 116: 250404. doi: 10.1103/PhysRevLett.116.250404
    [132]
    Liu B, Huang Y, Gong Y, et al. Experimental demonstration of quantum contextuality with nonentangled photons. Physical Review A, 2009, 80: 044101. doi: 10.1103/PhysRevA.80.044101
    [133]
    Cabello A. Proposed test of macroscopic quantum contextuality. Physical Review A, 2010, 82: 032110. doi: 10.1103/PhysRevA.82.032110
    [134]
    Vidick T, Wehner S. Does ignorance of the whole imply ignorance of the parts? Large violations of noncontextuality in quantum theory. Physical Review Letters, 2011, 107: 030402. doi: 10.1103/PhysRevLett.107.030402
    [135]
    Amaral B, Cunha M T, Cabello A. Quantum theory allows for absolute maximal contextuality. Physical Review A, 2015, 92: 062125. doi: 10.1103/PhysRevA.92.062125
    [136]
    Mermin N D. Extreme quantum entanglement in a superposition of macroscopically distinct states. Physical Review Letters, 1990, 65: 1838. doi: 10.1103/PhysRevLett.65.1838
    [137]
    Ardehali M. Bell inequalities with a magnitude of violation that grows exponentially with the number of particles. Physical Review A, 1992, 46: 5375–5378. doi: 10.1103/PhysRevA.46.5375
    [138]
    Belinskiĭ A, Klyshko D N. Interference of light and Bell’s theorem. Physics-Uspekhi, 1993, 36: 653. doi: 10.1070/pu1993v036n08abeh002299
    [139]
    Cavalcanti E G. Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning. Physical Review X, 2018, 8: 021018. doi: 10.1103/PhysRevX.8.021018
    [140]
    Pearl J, Cavalcanti E. Classical causal models cannot faithfully explain Bell nonlocality or Kochen-Specker contextuality in arbitrary scenarios. Quantum, 2021, 5: 518. doi: 10.22331/q-2021-08-05-518
    [141]
    Hu X M, Xie Y, Arora A S, et al. Self-testing of a single quantum system: Theory and experiment. [2022-03-01]. https://arxiv.org/abs/2203.09003v1.
    [142]
    Xu J S, Sun K, Pachos J K, et al. Photonic implementation of Majorana-based Berry phases. Science Advances, 2018, 4: eaat6533. doi: 10.1126/sciadv.aat6533
    [143]
    Liu C, Huang H L, Chen C, et al. Demonstration of topologically path-independent anyonic braiding in a nine-qubit planar code. Optica, 2019, 6: 264–268. doi: 10.1364/OPTICA.6.000264
    [144]
    Huang H L, Narożniak M, Liang F, et al. Emulating quantum teleportation of a Majorana zero mode qubit. Physical Review Letters, 2021, 126: 090502. doi: 10.1103/PhysRevLett.126.090502
    [145]
    Kirby W M, Tranter A, Love P J. Contextual subspace variational quantum eigensolver. Quantum, 2021, 5: 456. doi: 10.22331/q-2021-05-14-456
    [146]
    Widmann M, Lee S Y, Rendler T, et al. Coherent control of single spins in silicon carbide at room temperature. Nature Materials, 2015, 14: 164–168. doi: 10.1038/nmat4145
    [147]
    Wang J F, Yan F F, Li Q, et al. Coherent control of nitrogen-vacancy center spins in silicon carbide at room temperature. Physical Review Letters, 2020, 124: 223601. doi: 10.1103/PhysRevLett.124.223601
    [148]
    Wang J F, Yan F F, Li Q, et al. Robust coherent control of solid-state spin qubits using anti-Stokes excitation. Nature Communications, 2021, 12: 3223. doi: 10.1038/s41467-021-23471-8
    [149]
    Xu Z P, Saha D, Su H Y, et al. Reformulating noncontextuality inequalities in an operational approach. Physical Review A, 2016, 94: 062103. doi: 10.1103/PhysRevA.94.062103
    [150]
    Leifer M, Duarte C. Noncontextuality inequalities from antidistinguishability. Physical Review A, 2020, 101: 062113. doi: 10.1103/PhysRevA.101.062113
    [151]
    Lovász L, Saks M, Schrijver A. Orthogonal representations and connectivity of graphs. Linear Algebra and Its Applications, 1989, 114: 439–454. doi: 10.1016/0024-3795(89)90475-8

    Article Metrics

    Article views (811) PDF downloads(3503)
    Proportional views

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return