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Local Discrimination of Orthogonal Product States with a Two-Qubit Maximally Entangled State

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Abstract

Recently, Zhang et al. raised two classes of orthogonal product states which cannot be exactly discriminated by local operations and classical communication (LOCC) in the quantum system of (2k + 1) ⊗ 2l and (3k + i) ⊗ (3l + j) (Sci. Rep. 6, 28864, 2016). However, it remains a meaningful question that what entanglement resources are necessary and/or sufficient for this task to be possible with LOCC. In this paper, we present a method of using only an auxiliary 2 ⊗ 2 maximally entangled state to complete the local discrimination. Specifically, by utilizing a two-qubit maximally entangled state as an ancillary resource, we propose a concrete protocol respectively to locally identify orthogonal product states in 5 ⊗ 6 and 5 ⊗ 5. Then we generalize the distinguishing method respectively to the states in the quantum system of (2k + 1) ⊗ 2l and (3k + i) ⊗ (3l + j). These results can make us have a better understanding of the relationship between quantum entanglement and quantum nonlocality.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (Grants No. 61701343, No. 11701423 and No. 61771294) and Shandong Provincial Natural Science Foundation (Grant No. ZR2019MF023).

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Authors and Affiliations

  1. School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China

    Tian-Qing Cao & Lu Zhao

  2. School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China

    Qiao-Ling Xin

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  1. Tian-Qing Cao
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  2. Qiao-Ling Xin
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Correspondence to Tian-Qing Cao.

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Cao, TQ., Xin, QL. & Zhao, L. Local Discrimination of Orthogonal Product States with a Two-Qubit Maximally Entangled State. Int J Theor Phys 60, 1399–1415 (2021). https://doi.org/10.1007/s10773-021-04766-4

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