Abstract
Recently, the method that using an entanglement as a resource to distinguish orthogonal product states by local operations and classical communication (LOCC) has brought into focus. Zhang et al. (Sci Rep 6:30493, 2016) presented protocols which use an entanglement to distinguish some classes of orthogonal product states in \(\mathbb {C}^m\otimes \mathbb {C}^n\). In this paper, we mainly study the local distinguishability of multipartite product states. For the class of locally indistinguishable multipartite product states constructed by Wang et al. (Quantum Inf Process 16:5, 2017), we present a protocol that distinguishes perfectly these quantum states by LOCC using an entangled state as a resource for implementing quantum measurements.
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Ghosh, S., Kar, G., Roy, A., Sen, A., Sen, U.: Distinguishability of Bell states. Phys. Rev. Lett. 87, 277902 (2001)
Ghosh, S., Kar, G., Roy, A., Sarkar, D.: Distinguishability of maximally entangled states. Phys. Rev. A 70, 022304 (2004)
Hayashi, M., Markham, D., Murao, M., Owari, M., Virmani, S.: Bounds on multipartite entangled orthogonal state discrimination using local operations and classical communication. Phys. Rev. Lett. 96, 040501 (2006)
Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070 (1999)
Walgate, J., Hardy, L.: Nonlocality, asymmetry, and distinguishing bipartite states. Phys. Rev. Lett. 89, 147901 (2002)
Horodecki, M., Sen, A., Sen, U., Horodecki, K.: Local indistinguishability: more nonlocality with less entanglement. Phys. Rev. Lett. 90, 047902 (2003)
De Rinaldis, S.: Distinguishability of complete and unextendible product bases. Phys. Rev. A 70, 022309 (2004)
Nathanson, M.: Distinguishing bipartitite orthogonal states using LOCC: best and worst cases. J. Math. Phys. 46, 062103 (2005)
Niset, J., Cerf, N.J.: Multipartite nonlocality without entanglement in many dimensions. Phys. Rev. A 74, 052103 (2006)
Feng, Y., Shi, Y.: Characterizing locally indistinguishable orthogonal product states. IEEE Trans. Inf. Theory 55, 2799–2806 (2009)
Duan, R., Xin, Y., Ying, M.: Locally indistinguishable subspaces spanned by three-qubit unextendible product bases. Phys. Rev. A 81, 032329 (2010)
Childs, A.M., Leung, D., Mančinska, L., Ozols, M.: A framework for bounding nonlocality of state discrimination. Commun. Math. Phys. 323, 1121–1153 (2013)
Zhang, Z.C., Gao, F., Tian, G.J., Cao, T.Q., Wen, Q.Y.: Nonlocality of orthogonal product basis quantum states. Phys. Rev. A 90, 022313 (2014)
Wang, Y.L., Li, M.S., Zheng, Z.J., Fei, S.M.: Nonlocality of orthogonal product-basis quantum states. Phys. Rev. A 92, 032313 (2015)
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)
Zhang, Z.C., Gao, F., Cao, Y., Qin, S.J., Wen, Q.Y.: Local indistinguishability of orthogonal product states. Phys. Rev. A 93, 012314 (2016)
Xu, G.B., Yang, Y.H., Wen, Q.Y., Qin, S.J., Gao, F.: Constructing locally indistinguishable orthogonal product bases in an \( m\otimes n \) system(2015). arXiv:1512.06485
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)
Wang, Y.L., Li, M.S., Zheng, Z.J., Fei, S.M.: The local indistinguishability of multipartite product states. Quantum Inf. Process. 16, 5 (2017)
Zhang, X., Weng, J., Tan, X., Luo, W.: Indistinguishability of pure orthogonal product states by LOCC. Quantum Inf. Process. 16, 168 (2017)
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)
Cohen, S.M.: Understanding entanglement as resource: locally distinguishing unextendible product bases. Phys. Rev. A 77, 012304 (2008)
Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661 (1991)
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)
Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394 (1998)
Kim, Y.H., Kulik, S.P., Shih, Y.: Quantum teleportation of a polarization state with a complete Bell state measurement. Phys. Rev. Lett. 86, 1370 (2001)
Wang, C., Deng, F.G., Long, G.L.: Multi-step quantum secure direct communication using multi-particle Green–Horne–Zeilinger state. Opt. Commun. 253, 15–20 (2005)
Tian-Yin, W., Su-Juan, Q., Qiao-Yan, W., Fu-Chen, Z.: Analysis and improvement of multiparty controlled quantum secure direct communication protocol. Acta. Physica Sinica. 57(12), 135–137 (2008)
Yang, C.W., Tsai, C.W., Hwang, T.: Fault tolerant two-step quantum secure direct communication protocol against collective noises. Sci. China Phys. 54, 496–501 (2011)
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)
Li, Z.G., Zhao, M., Li, S.M., Wang, H., Liu, W.M.: Maximally entangled state can be a mixed state. Quant. Inf. Comput 12, 0063–0073 (2012)
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Li, HQ., Jing, Nh. & Tang, XL. Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource. Quantum Inf Process 17, 195 (2018). https://doi.org/10.1007/s11128-018-1962-2
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DOI: https://doi.org/10.1007/s11128-018-1962-2