Local Discrimination of Orthogonal Product States with a Two-Qubit Maximally Entangled State
Tóm tắt
Recently, Zhang et al. raised two classes of orthogonal product states which cannot be exactly discriminated by local operations and classical communication (LOCC) in the quantum system of (2k + 1) ⊗ 2l and (3k + i) ⊗ (3l + j) (Sci. Rep. 6, 28864, 2016). However, it remains a meaningful question that what entanglement resources are necessary and/or sufficient for this task to be possible with LOCC. In this paper, we present a method of using only an auxiliary 2 ⊗ 2 maximally entangled state to complete the local discrimination. Specifically, by utilizing a two-qubit maximally entangled state as an ancillary resource, we propose a concrete protocol respectively to locally identify orthogonal product states in 5 ⊗ 6 and 5 ⊗ 5. Then we generalize the distinguishing method respectively to the states in the quantum system of (2k + 1) ⊗ 2l and (3k + i) ⊗ (3l + j). These results can make us have a better understanding of the relationship between quantum entanglement and quantum nonlocality.
Tài liệu tham khảo
Bennett, C. H., Divincenzo, D. P., Fuchs, C. A., Mor, T., Rains, E., Shor, P. W., Smolin, J. A.: Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070 (1999)
Walgate, J., Short, A. J., Hardy, L., Vedral, V.: Local distinguishability of multipartite orthogonal quantum states. Phys. Rev. Lett. 85, 4972 (2000)
Duan, R. Y., Feng, Y., Xin, Y., Ying, M. S.: Distinguishability of quantum states by separable operations. IEEE Trans. Inf. Theory 55, 1320 (2009)
Gao, F., Liu, B., Huang, W., Wen, Q. Y.: Postprocessing of the oblivious key in quantum private query. IEEE J. Sel. Top. Quantum Electron. 21, 98 (2015)
Wei, C. Y., Wang, T. Y., Gao, F.: Practical quantum private query with better performance in resisting joint-measurement attack. Phys. Rev. A 93, 042318 (2016)
Fan, H.: Distinguishability and indistinguishability by local operations and classical communication. Phys. Rev. Lett. 92, 177905 (2004)
Watrous, J.: Bipartite subspaces having no bases distinguishable by local operations and classical communication. Phys. Rev. Lett. 95, 080505 (2005)
Fan, H.: Distinguishing bipartite states by local operations and classical communication. Phys. Rev. A 75, 014305 (2007)
Bandyopadhyay, S., Ghosh, S., Kar, G.: LOCC distinguishability of unilaterally transformable quantum states. New. J. Phys. 13, 123013 (2011)
Yu, N. K., Duan, R. Y., Ying, M. S.: Four locally indistinguishable ququad-ququad orthogonal maximally entangled states. Phys. Rev. Lett. 109, 020506 (2012)
Cosentino, A.: Positive-partial-transpose-indistinguishable states via semidefinite programming. Phys. Rev. A 87, 012321 (2013)
Lebl, J., Shakeel, A., Wallach, N.: Local distinguishability of generic unentangled orthonormal bases. Phys. Rev. A 93, 012330 (2016)
Horodecki, M., Sen(De), A., Sen, U.: Horodecki, K.: Local indistinguishability: more nonlocality with less entanglement. Phys. Rev. Lett. 90, 047902 (2003)
Feng, Y., Shi, Y. Y.: Characterizing locally indistinguishable orthogonal product states. IEEE Trans. Inf. Theory 55, 2799 (2009)
Bandyopadhyay, S.: More nonlocality with less purity. Phys. Rev. Lett. 106, 210402 (2011)
Childs, A. M., Leung, D., Mančinska, L., Ozols, M.: A framework for bounding nonlocality of state discrimination. Commun. Math. Phys. 323, 1121 (2013)
Zhang, Z. C., Gao, F., Qin, S. J., Yang, Y. H., Wen, Q. Y.: Nonlocality of orthogonal product states. Phys. Rev. A 92, 012332 (2015)
Xu, G. B., Wen, Q. Y., Qin, S. J., Yang, Y. H., Gao, F.: Quantum nonlocality of multipartite orthogonal product states. Phys. Rev. A 93, 032341 (2016)
Zhang, X. Q., Tan, X. Q., Weng, J., Li, Y. J.: LOCC indistinguishable orthogonal product quantum states. Sci. Rep. 6, 28864 (2016)
Zhang, Z. C., Zhang, K. J., Gao, F., Wen, Q. Y., Oh, C. H.: Construction of nonlocal multipartite quantum states. Phys. Rev. A 95, 052344 (2017)
Jiang, D. H., Xu, G. B.: Nonlocal sets of orthogonal product states in an arbitrary multipartite quantum system. Phys. Rev. A 102, 032211 (2020)
Cohen, S. M.: Understanding entanglement as resource: locally distinguishing unextendible product bases. Phys. Rev. A 77, 012304 (2008)
Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W. K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
Bandyopadhyay, S., Brassard, G., Kimmel, S., Wootters, W. K.: Entanglement cost of nonlocal measurements. Phys. Rev. A 80, 012313 (2009)
Bennett, C. H., Wiesner, S. J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)
DiVincenzo, D. P., Leung, D. W., Terhal, B. M.: Quantum data hiding. IEEE Trans. Inf. Theory 48, 580 (2002)
Matthews, W., Wehner, S., Winter, A.: Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding. Commun. Math. Phys. 291, 813 (2009)
Zhang, Z. C., Gao, F., Cao, T. Q., Qin, S. J., Wen, Q. Y.: Entanglement as a resource to distinguish orthogonal product states. Sci. Rep. 6, 30493 (2016)
Bandyopadhyay, S., Halder, S., Nathanson, M.: Entanglement as a resource for local state discrimination in multipartite systems. Phys. Rev. A 94, 022311 (2016)
Güngör, Ö., Turgut, S.: Entanglement-assisted state discrimination and entanglement preservation. Phys. Rev. A 94, 032330 (2016)
Zhang, Z. C., Song, Y. Q., Song, T. T., Gao, F., Qin, S. J., Wen, Q. Y.: Local distinguishability of orthogonal quantum states with multiple copies of 2 ⊗ 2 maximally entangled states. Phys. Rev A 97, 022334 (2018)
Li, H. Q., Jing, N. H., Tang, X. L.: Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource. Quantum Inf. Process. 17, 195 (2018)
Li, L. J., Gao, F., Zhang, Z. C., Wen, Q. Y.: Local distinguishability of orthogonal quantum states with no more than one ebit of entanglement. Phys. Rev. A 99, 012343 (2019)
Li, L. J., Gao, F., Zhang, Z. C., Wen, Q. Y.: Using entanglement more efficiently in distinguishing orthogonal product states by LOCC. Quantum Inf. Process. 18, 330 (2019)