Abstract
We concentrate on the differences between one-way local operations and classical communication (1-LOCC) and two-way local operations and classical communication (2-LOCC) in distinguishing maximally entangled states (MESs). We analyze the 2-LOCC distinguishability of k MESs which were constructed by using 1-LOCC indistinguishable qubit lattice states (LSs) (Nathanson in Phys Rev A 88:062316, 2013). We give a sufficient condition that illustrates which type of Nathanson’s constructed states can be distinguished by 2-LOCC. It partly solves an open question proposed by Nathanson. Furthermore, we answer the question in a simpler and more efficient way, at least to some extent. That is, the k constructed states can be distinguished by 2-LOCC but not by 1-LOCC if \(k(k-1)-m(m-1)< 2^{r+2}\), where the initial LSs are in \({\mathbb {C}}^{2^{r}}\otimes {\mathbb {C}}^{2^{r}}\) and m is the largest number of pairwise commuting matrices corresponding to the initial LSs. Finally, we find an interesting phenomenon, i.e., 1-LOCC and 2-LOCC work differently when distinguishing four ququad-ququad LSs and distinguishing four constructed states derived from the four LSs. For the four ququad-ququad LSs, 2-LOCC has no advantage over 1-LOCC. However, for the four constructed states, 2-LOCC has advantages over 1-LOCC.
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Acknowledgements
This work is supported by NSFC (Grant Nos. 61601171, 11971151, 11901163, 61701343), Open Foundation of State key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) (SKLNST-2019-2-18), Foundation of Doctor of Henan Polytechnic University (B2017-48), Project of Science and Technology Department of Henan Province of China (182102210306), Natural Science Foundation of Shandong Province (ZR2019MF023). Ying-Hui Yang is also supported by the Government of China through CSC.
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Yang, YH., Yuan, JT., Wang, CH. et al. Locally distinguishable maximally entangled states by two-way LOCC. Quantum Inf Process 20, 18 (2021). https://doi.org/10.1007/s11128-020-02957-2
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DOI: https://doi.org/10.1007/s11128-020-02957-2