Local Unitary Invariants for Multipartite States |
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Authors: | Ting-Gui Zhang Ming-Jing Zhao Xianqing Li-Jost Shao-Ming Fei |
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Affiliation: | 1. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany 2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China
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Abstract: | We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For multipartite mixed states, we propose a set of invariants in terms of the trace of coefficient matrices. For full rank mixed states with non-degenerate eigenvalues, this set of invariants is also the set of the necessary and sufficient conditions for the local unitary equivalence of such two states. |
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