Locally distinguishing genuinely nonlocal sets with entanglement resource

Qiao Qiao; Su-Juan Zhang; Chen-Ming Bai; Lu Liu

doi:10.1088/1572-9494/ad6de6

PDF(323 KB)

Communications in Theoretical Physics ›› 2024, Vol. 76 ›› Issue (12) : 125101. DOI: 10.1088/1572-9494/ad6de6

Quantum Physics and Quantum Information

Locally distinguishing genuinely nonlocal sets with entanglement resource

Author information +

History +

Abstract

A set of orthogonal product states is deemed genuinely nonlocal if they remain locally indistinguishable under any bipartition. In this paper, we first construct a genuinely nonlocal product basis B_I(5, 3) in $C^{5} \otimes C^{5} \otimes C^{5}$ using a set of nonlocal product states in $C^{3} \otimes C^{4}$ . Then, we obtain a genuinely nonlocal product basis B_II(5, 3) by replacing certain states in B_I(5, 3) with some superposition states. We achieve perfect discrimination of the constructed genuinely nonlocal product basis, separately employing two EPR states and one GHZ state. Our protocol is more efficient than quantum teleportation.

Key words

local discrimination / genuinely nonlocal / entanglement-assisted discrimination

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

Qiao Qiao, Su-Juan Zhang, Chen-Ming Bai, et al. Locally distinguishing genuinely nonlocal sets with entanglement resource[J]. Communications in Theoretical Physics, 2024, 76(12): 125101 https://doi.org/10.1088/1572-9494/ad6de6

References

List( Publishing order | Descend order by publishing year | Descend order by cited within ) Chart analysis

1	Ke W 2023 A receipt-free quantum voting protocol based on quantum public key encryption and quantum key agreement Phys. Scr. 98 065112 https://doi.org/10.1088/1402-4896/acd3bd Cited in this article [1]

2	Ha D, Kim J S 2024 Nonlocal quantum state ensembles and quantum data hiding Phys. Rev. A 109 052418 https://doi.org/10.1103/PhysRevA.109.052418 Cited in this article [1]

3	Lami L 2021 Quantum data hiding with continuous-variable systems Phys. Rev. A 104 052428 https://doi.org/10.1103/PhysRevA.104.052428 Cited in this article [1]

4	Shen A 2023 Experimental quantum secret sharing based on phase encoding of coherent states Sci. China G 66 260311 https://doi.org/10.1007/s11433-023-2105-7 Cited in this article [1]

5	Bai C M, Zhang S, Liu L 2022 Quantum secret sharing based on quantum information masking Quantum Inf. Process. 21 377 https://doi.org/10.1007/s11128-022-03723-2

6	Lin J, Chen C C, Huang C Y 2024 Efficient dynamic quantum secret sharing in pre-measurement and post-measurement phases Physica A 638 129615 https://doi.org/10.1016/j.physa.2024.129615 Cited in this article [1]

7	Bennett C H 1999 Quantum nonlocality without entanglement Phys. Rev. A 59 1070 https://doi.org/10.1103/PhysRevA.59.1070 Cited in this article [1]

8	Bennett C H 1999 Unextendible product bases and bound entanglement Phys. Rev. Lett. 82 5385 https://doi.org/10.1103/PhysRevLett.82.5385 Cited in this article [1]

9	Kupczynski M 2024 Quantum nonlocality: how does nature do it? Entropy 26 191 https://doi.org/10.3390/e26030191

10	DiVincenzo D P 2003 Unextendible product bases, uncompletable product bases and bound entanglement Commun. Math. Phys. 238 379 410 https://doi.org/10.1007/s00220-003-0877-6 Cited in this article [1]

11	Zhu Y Y 2023 Completable sets of orthogonal product states with minimal nonlocality Physica A 624 128956 https://doi.org/10.1016/j.physa.2023.128956

12	Halder S, Streltsov A 2023 Unextendibility, uncompletability, and many-copy indistinguishable ensembles arXiv:2303.17507

13	Xu G B, Jiang D H 2021 Novel methods to construct nonlocal sets of orthogonal product states in an arbitrary bipartite high-dimensional system Quantum Inf. Process. 20 128 https://doi.org/10.1007/s11128-021-03062-8 Cited in this article [2]

14	Zhen X F, Fei S M, Zuo H J 2022 Nonlocality without entanglement in general multipartite quantum systems Phys. Rev. A 106 062432 https://doi.org/10.1103/PhysRevA.106.062432 Cited in this article [1]

15	Shi F 2022 Strong quantum nonlocality in N-partite systems Phys. Rev. A 105 022209 https://doi.org/10.1103/PhysRevA.105.022209

16	Halder S 2018 Several nonlocal sets of multipartite pure orthogonal product states Phys. Rev. A 98 022303 https://doi.org/10.1103/PhysRevA.98.022303 Cited in this article [1]

17	Xu G B 2017 Local indistinguishability of multipartite orthogonal product bases Quantum Inf. Process. 16 276 https://doi.org/10.1007/s11128-017-1725-5

18	Wang Y L 2017 The local indistinguishability of multipartite product states Quantum Inf. Process. 16 5 https://doi.org/10.1007/s11128-016-1477-7 Cited in this article [1]

19	Rout S 2021 Multiparty orthogonal product states with minimal genuine nonlocality Phys. Rev. A 104 052433 https://doi.org/10.1103/PhysRevA.104.052433

20	Halder S 2018 Several nonlocal sets of multipartite pure orthogonal product states Phys. Rev. A 98 022303 https://doi.org/10.1103/PhysRevA.98.022303 Cited in this article [1]

21	Halder S 2019 Strong quantum nonlocality without entanglement Phys. Rev. Lett. 122 040403 https://doi.org/10.1103/PhysRevLett.122.040403 Cited in this article [2]

22	Xiong Z X 2023 Distinguishability-based genuine nonlocality with genuine multipartite entanglement Phys. Rev. A 108 022405 https://doi.org/10.1103/PhysRevA.108.022405 Cited in this article [1]

23	Xiong Z X 2024 Small sets of genuinely nonlocal Greenberger–Horne–Zeilinger states in multipartite systems Phys. Rev. A 109 022428 https://doi.org/10.1103/PhysRevA.109.022428 Cited in this article [1]

24	Walgate J, Short A J, Hardy L, Vedral V 2000 Local distinguishability of multipartite orthogonal quantum states Phys. Rev. Lett. 85 4972 https://doi.org/10.1103/PhysRevLett.85.4972 Cited in this article [1]

25	Chen Y X, Yang D 2002 Optimally conclusive discrimination of nonorthogonal entangled states by local operations and classical communications Phys. Rev. A 65 022320 https://doi.org/10.1103/PhysRevA.65.022320 Cited in this article [1]

26	Bennett C H 1993 Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels Phys. Rev. Lett. 70 1895 https://doi.org/10.1103/PhysRevLett.70.1895 Cited in this article [1]

27	Cohen S M 2008 Understanding entanglement as resource: locally distinguishing unextendible product bases Phys. Rev. A 77 012304 https://doi.org/10.1103/PhysRevA.77.012304 Cited in this article [2]

28	Zhang Z C 2016 Entanglement as a resource to distinguish orthogonal product states Sci. Rep. 6 30493 https://doi.org/10.1038/srep30493 Cited in this article [1]

29	Li L J 2019 Local distinguishability of orthogonal quantum states with no more than one ebit of entanglement Phys. Rev. A 99 012343 https://doi.org/10.1103/PhysRevA.99.012343 Cited in this article [1]

30	Yuan P, Tian G, Sun X 2020 Strong quantum nonlocality without entanglement in multipartite quantum systems Phys. Rev. A 102 042228 https://doi.org/10.1103/PhysRevA.102.042228 Cited in this article [1]

31	Mao Y L 2022 Test of genuine multipartite nonlocality Phys. Rev. Lett. 129 150401 https://doi.org/10.1103/PhysRevLett.129.150401

32	Cao H Q, Zuo H J 2023 Locally distinguishing nonlocal sets with entanglement resource Physica A 623 128852 https://doi.org/10.1016/j.physa.2023.128852

33	Zhu C 2024 Entanglement cost of discriminating quantum states under locality constraints arXiv:2402.18446

34	Piveteau A 2022 Entanglement-assisted quantum communication with simple measurements Nat. Commun. 13 7878 https://doi.org/10.1038/s41467-022-33922-5 Cited in this article [1]

35	Rout S 2019 Genuinely nonlocal product bases: classification and entanglement-assisted discrimination Phys. Rev. A 100 032321 https://doi.org/10.1103/PhysRevA.100.032321 Cited in this article [4]

Acknowledgments

We would like to express our gratitude to the anonymous referees for their valuable and constructive comments. This work was supported by the National Natural Science Foundation of China under grant 12301590, and the Natural Science Foundation of Hebei Province under grant A2022210002.