Local unitary invariants for multipartite states
Ting-Gui Zhang, Ming-Jing Zhao, Xianqing Li-Jost, and Shao-Ming Fei
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Submission date: 07. Aug. 2013
published in: International journal of theoretical physics, 52 (2013) 9, p. 3020-3025
DOI number (of the published article): 10.1007/s10773-013-1593-4
PACS-Numbers: 03.67.-a, 02.20.Hj, 03.65.-w
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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 ranked mixed states with nondegenerate eigenvalues, this set of invariants is also the necessary and sufficient conditions for the local unitary equivalence of such two states.