Abstract
In this letter, we mainly study the local indistinguishability of mutually orthogonal maximally entangled states, which are in canonical form. Firstly, we present a feasible sufficient and necessary condition for distinguishing such states by one-way local operations and classical communication (LOCC). Secondly, for the application of this condition, we exhibit one class of maximally entangled states that can be locally distinguished with certainty. Furthermore, sets of \(d-1\) indistinguishable maximally entangled states by one-way LOCC are demonstrated in \(d \otimes d\) (for \(d=7, 8, 9, 10\)). Interestingly, we discover there exist sets of \(d-2\) such states in \(d \otimes d\) (for \(d=8, 9, 10\)), which are not perfectly distinguishable by one-way LOCC. Finally, we conjecture that there exist \(d-1\) or fewer indistinguishable maximally entangled states in \(d \otimes d(d \ge 5)\) by one-way LOCC.
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References
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(2), 1070–1091 (1999)
Bennett, C.H., DiVincenzo, D.P., Mor, T., Shor, P.W., Smolin, J.A., Terhal, B.M.: Unextendible product bases and bound entanglement. Phys. Rev. Lett. 82(26), 5385–5388 (1999)
Walgate, J., Hardy, L.: Nonlocality, asymmetry and distinguishing bipartite states. Phys. Rev. Lett. 89(14), 147901 (2002)
Horodecki, M., De Sen, A., Sen, U., Horodecki, K.: Local distinguishability: more nonlocality with less entanglement. Phys. Rev. Lett. 90(4), 047902 (2003)
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(8), 040501 (2006)
Ghosh, S., Kar, G., Roy, A., De Sen, A., Sen, U.: Distinguishability of Bell states. Phys. Rev. Lett. 87(27), 277902 (2001)
Fan, H.: Distinguishability and indistinguishability by local operations and classical communication. Phys. Rev. Lett. 92(17), 177905 (2004)
Nathanson, M.: Distinguishing bipartite orthogonal states by LOCC: best and worst cases. J. Math. Phys. 46(6), 062103 (2005)
Owari, M., Hayashi, M.: Local copying and local discrimination as a study for nonlocality of a set of states. Phys. Rev. A 74(3), 032108 (2006)
Walgate, J., Short, A.J., Hardy, L., Vedral, V.: Local distinguishability of multipartite orthogonal quantum states. Phys. Rev. Lett. 85(23), 4972–4975 (2000)
Ghosh, S., Kar, G., Roy, A., Sarkar, D.: Distinguishability of maximally entangled states. Phys. Rev. A 70(2), 022304 (2004)
Bandyopadhyay, S., Ghosh, S., Kar, G.: LOCC distinguishability of unilaterally transformable quantum states. New J. Phys. 13(12), 123013 (2011)
Yu, N., Duan, R.Y., Ying, M.S.: Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States. Phys. Rev. Lett. 109(2), 020506 (2012)
Cosentino, A.: Positive-partial-transpose-indistinguishable states via semidefinite programming. Phys. Rev. A 87(1), 012321 (2013)
Acknowledgments
This work is supported by NSFC (Grant Nos. 61272057, 61202434, 61170270, 61100203, 61003286, 61121061), NCET (Grant No. NCET-10-0260), Beijing Natural Science Foundation (Grant Nos. 4112040, 4122054), the Fundamental Research Funds for the Central Universities (Grant No. 2012RC0612, 2011YB01).
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Zhang, ZC., Wen, QY., Gao, F. et al. One-way LOCC indistinguishability of maximally entangled states. Quantum Inf Process 13, 795–804 (2014). https://doi.org/10.1007/s11128-013-0691-9
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DOI: https://doi.org/10.1007/s11128-013-0691-9