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Locally distinguishing nonlocal orthogonal product states with entanglement as a universal auxiliary resource

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Abstract

Recently, three classes of orthogonal product states in \(\mathbb {C}^m\otimes \mathbb {C}^n(m\ge 3, n\ge 3)\) which cannot be exactly discriminated by local operations and classical communication (LOCC) have been constructed, respectively, by Xu et al. (Quantum Inf. Process. 20: 128, 2021) and Zhu et al. (Physica A 624: 128956, 2023). However, it is interesting to know, in order to perfectly distinguish these states by LOCC, how much entanglement resources are sufficient and/or necessary and whether it is possible to find a universal auxiliary resource. In this paper, we present that by using only one two-qubit maximally entangled state as a general auxiliary resource, the above locally indistinguishable states can all be perfectly identified by LOCC. And the general process of auxiliary local discrimination using entanglement is discussed in detail. The local distinguishing protocols we designed not only utilize minimal amount of assisted entanglement, but also show that the strength of these nonlocal sets is minimal from the point of view of auxiliary resources.

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Data Availability

No datasets were generated or analysed during the current study.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grants No. 61701343 and No. 11701423) and the Natural Science Foundation of Tianjin (Grant No. 23JCQNJC01150).

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Authors and Affiliations

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

    Tian-Qing Cao, Bo-Hui Gao & 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. Bo-Hui Gao
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  3. Qiao-Ling Xin
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  4. Lu Zhao
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Contributions

T.Q.C. and Q.L.X. initiated the idea. T.Q.C., B.H.G. and L.Z. wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Tian-Qing Cao.

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Cao, TQ., Gao, BH., Xin, QL. et al. Locally distinguishing nonlocal orthogonal product states with entanglement as a universal auxiliary resource. Quantum Inf Process 24, 104 (2025). https://doi.org/10.1007/s11128-025-04727-4

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