Nonlocality of orthogonal product basis quantum states

Yan-Ling Wang, Mao-Sheng Li, Zhu-Jun Zheng, and Shao-Ming Fei

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Submission date: 25. Aug. 2015
Pages: 7
published in: Physical review / A, 92 (2015) 3, art-no. 032313 
DOI number (of the published article): 10.1103/PhysRevA.92.032313
Bibtex
PACS-Numbers: 03.67.Hk, 03.65.Ud
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Abstract:
We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of ℂ^d ⊗ ℂ^d, where d is odd, Zhang et al have constructed d² orthogonal product basis quantum states which are locally indistinguishable in [Phys. Rev. A. 90, 022313(2014)]. We find a subset contains with 6d − 9 orthogonal product states which are still locally indistinguishable. Then we generalize our method to arbitrary bipartite quantum system ℂ^m ⊗ ℂⁿ. We present a small set with only 3(m + n) − 9 orthogonal product states and prove these states are 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.