Nonlocality of orthogonal product-basis quantum states

Yan-Ling Wang, Mao-Sheng Li, Zhu-Jun Zheng, and Shao-Ming Fei
Phys. Rev. A 92, 032313 – Published 10 September 2015

Abstract

We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of CdCd, where d is odd, Zhang et al. [Z.-C. Zhang et al., Phys. Rev. A 90, 022313 (2014)] have constructed d2 orthogonal product basis quantum states that are locally indistinguishable. We find a subset that contains 6d9 orthogonal product states that are still locally indistinguishable. We generalize our method to an arbitrary bipartite quantum system CmCn. We present a small set with only 3(m+n)9 orthogonal product states and prove that these states are local operations and classical communication (LOCC) indistinguishable. Even though these 3(m+n)9 product states are LOCC indistinguishable, they can be distinguished by separable measurements. This shows that separable operations are strictly stronger than the local operations and classical communication.

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  • Received 18 March 2015

DOI:https://doi.org/10.1103/PhysRevA.92.032313

©2015 American Physical Society

Authors & Affiliations

Yan-Ling Wang1, Mao-Sheng Li1, Zhu-Jun Zheng1, and Shao-Ming Fei2,3

  • 1Department of Mathematics, South China University of Technology, Guangzhou 510640, China
  • 2School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 3Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany

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Vol. 92, Iss. 3 — September 2015

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