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arXiv:2003.10627 · International Journal of Theoretical Physics

Local Unitary Invariants of Quantum States

Meiyu Cui, Jingmei Chang, Ming‐Jing Zhao, Xiaofen Huang, Tinggui Zhang

Published Sep 11, 2017• 6 citations
arXivHTMLPDF
DOI
10.1007/s10773-017-3523-3

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Local unitary (LU) equivalent states are crucial for understanding the structure of quantum entanglement. We investigate the LU equivalence based on the LU Bargmann invariants (LUBIs). We consider for which states the LUBIs are sufficient to ensure the LU equivalence. We focus on a class of multipartite states with complete local commutativity, called CLC states. We first show that for multipartite CLC states, all the LUBIs are sufficient to ensure the local permutation equivalence, if their single-party marginals are diagonal and non-degenerate. By virtue of the fact that the CLC property remains unchanged under local operations, we verify that the LUBIs are also sufficient to ensure the LU equivalence of multipartite CLC states whose single-party marginals are non-degenerate. Furthermore, when the single-party marginals are degenerate, we propose concrete examples of two-qudit and three-qubit systems, showing that there are states which share all the LUBIs but are not LU equivalent.