Locally distinguishable maximally entangled states by two-way LOCC

• Published in: Quantum information processing 2021, Vol.20 (1), Article 18
• Main Authors: Yang, Ying-Hui, Yuan, Jiang-Tao, Wang, Cai-Hong, Geng, Shi-Jiao
• Format: Article
• Language: English
• Subjects: Data Structures and Information Theory; Entangled states; Mathematical Physics; Physics; Physics and Astronomy; Quantum Computing; Quantum Information Technology; Quantum Physics; Questions; Spintronics
• ISSN: 1570-0755; 1573-1332
• DOI: 10.1007/s11128-020-02957-2

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 C 2 r ⊗ 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.