Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations

Zuhuan Yu, Xianqing Li-Jost, and Shao-Ming Fei

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Submission date: 27. Aug. 2007
Pages: 12
published in: International journal of quantum information, 5 (2007) 6, p. 795-803 
DOI number (of the published article): 10.1142/S0219749907003262
Bibtex
PACS-Numbers: 03.67.-a, 02.20.Hj, 03.65.-w
Keywords and phrases: Schmidt decomposition, Bipartite mixed state, Local invariant, Representation class
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Abstract:
We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local unitary transformations if and only if they have the same representation class. Detailed examples are given on calculating representation classes.