Abstract
Nonlocality is one of the distinctive features of quantum mechanics and has different forms in practice, e.g., non-separability, quantum steering, and Bell nonlocality. Here, by exploiting the high-dimensional probability tensor, we propose a quantum magic square model to characterize the diverse forms of nonlocal phenomena in a single protocol. In this model, the nonlocalities are manifested in the partial-sums of the probability tensor, where the uncertainty relation serves as an “indicator” of different nonlocal phenomena. We derive a conditional majorization uncertainty relation criterion to witness the quantum steering. The new criterion is applicable to infinite number of observables and is found superior to the formerly thought optimal steering criterion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)
Schrödinger, E.: Discussion of probability relations between separated systems. Proc. Camb. Philosophical Soc. 31, 555–563 (1935)
Bell, J.S.: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964)
Wiseman, H.M., Jones, S.J., Doherty, A.C.: Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. Phys. Rev. Lett. 98, 140402 (2007)
Clauser, J. F., Horne, M. A., Shimony, A., Holt, R. A.: Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880-884 (1969); Erratum Phys. Rev. Lett. 24, 549 (1970)
Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrary high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)
Uola, R., Costa, A.C.S., Nguyen, H.C., Gühne, O.: Quantum steering. Rev. Mod. Phys. 92, 15001 (2020)
Li, Jun-Li, Qiao, Cong-Feng: A necessary and sufficient criterion for the separability of quantum state. Sci. Rep. 8, 1442 (2018)
Terhal, B.M.: Bell inequalities and the separability criterion. Phys. Lett. A 271, 319–326 (2000)
Cavalcanti, E.G., Foster, C.J., Fuwa, M., Wisema, H.M.: Analog of the Clauser-Horne-Shimony-Holt inequality for steering. J. Opt. Soc. Am. B 32, A74–A81 (2015)
Hofmann, H.F., Takeuchi, S.: Violation of local uncertainty relations as a signature of entanglement. Phys. Rev. A 68, 032103 (2003)
Cavalcanti, E.G., Jones, S.J., Wiseman, H.M., Reid, M.D.: Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox. Phys. Rev. A 80, 032112 (2009)
Gühne, O., Hyllus, P., Gittsovich, O., Eisert, J.: Covariance matrices and the separability problem. Phys. Rev. Lett. 99, 130504 (2007)
Kogias, I., Skrzypczyk, P., Cavalcanti, D., Acín, A., Adesso, G.: Hierarchy of steering criteria based on moments for all bipartite quantum systems. Phys. Rev. Lett. 115, 210401 (2015)
Costa, A.C.S., Uola, R., Gühne, O.: Entropic steering criteria: applications to bipartite and tripartite systems. Entropy 2, 763 (2018)
Coles, P.J., Berta, M., Tomamichel, M., Wehner, S.: Entropic uncertainty relations and their applications. Rev. Mod. Phys. 89, 015002 (2017)
Li, Jun-Li, Qiao, Cong-Feng: The optimal uncertainty relation. Ann. Phys. 531, 1900143 (2019)
Fine, A.: Hidden variables, joint probability, and the Bell inequalities. Phys. Rev. Lett. 48, 291–295 (1982)
Li, Jun-Li, Qiao, Cong-Feng: An optimal measurement strategy to beat the quantum uncertainty in correlated system. Adv. Quantum Technol. 3, 2000039 (2020)
Pusey, M.F.: Negativity and steering: a stronger Peres conjecture. Phys. Rev. A 88, 032313 (2013)
Costa, A.C.S., Uola, R., Gühne, O.: Steering criteria from general entropic uncertainty relations. Phys. Rev. A 98, 050104(R) (2018)
Yang, Ma-Cheng, Li, Jun-Li, Qiao, Cong-Feng: The decomposition of Werner and isotropic states, arXiv: 2003.00694
Acknowledgements
This work was supported in part by the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No.XDB23030100; and by the National Natural Science Foundation of China(NSFC) under the Grants 11975236 and 11635009.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Li, JL., Qiao, CF. Characterizing quantum nonlocalities per uncertainty relation. Quantum Inf Process 20, 109 (2021). https://doi.org/10.1007/s11128-021-03043-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-021-03043-x