Nonlocality of orthogonal product states

Zhi-Chao Zhang, Fei Gao, Su-Juan Qin, Ying-Hui Yang, and Qiao-Yan Wen
Phys. Rev. A 92, 012332 – Published 29 July 2015

Abstract

In this paper, we mainly study the local indistinguishability of mutually orthogonal product basis quantum states in dd. In 33, Bennett et al. [ Phys. Rev. A 59, 1070 (1999)] presented nine orthogonal product basis quantum states which cannot be distinguished by local operations and classical communication (LOCC). In the work by Zhang et al. [Z.-C. Zhang et al., Phys. Rev. A 90, 022313 (2014)], this result was generalized in dd, where d is odd. In this paper, we aim to construct locally indistinguishable orthogonal product basis quantum states in dd. For the general dd(d>2) quantum system, we first construct 4d4 orthogonal product states, and prove these states are locally indistinguishable using a very simple but quite effective method. Then, based on these states, we construct some classes of locally indistinguishable orthogonal product basis quantum states (OPBS) in dd(d>2). Finally, we construct some LOCC indistinguishable OPBS in multipartite quantum systems. All of the above results demonstrate the phenomenon of nonlocality without entanglement.

  • Received 12 April 2015

DOI:https://doi.org/10.1103/PhysRevA.92.012332

©2015 American Physical Society

Authors & Affiliations

Zhi-Chao Zhang1,*, Fei Gao1,†, Su-Juan Qin1, Ying-Hui Yang1,2, and Qiao-Yan Wen1

  • 1State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • 2School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

  • *zhichao1234@bupt.edu.cn
  • gaofei_bupt@hotmail.com

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Vol. 92, Iss. 1 — July 2015

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