Differential Geometry of Bipartite Quantum States
Zuhuan Yu, Xianqing Li-Jost, Qingzhong Li, Jintao Lv, and Shao-Ming Fei
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Submission date: 05. Apr. 2007
published in: Reports on mathematical physics, 60 (2007) 1, p. 125-133
DOI number (of the published article): 10.1016/S0034-4877(07)80104-2
PACS-Numbers: 03.67.-a, 03.65.Ud, 02.40.-k
Keywords and phrases: differential geometry, bipartite states, Manifold
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We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given Schmidt ranks or Schmidt coefficients are explicitly presented. The dimensions of the related manifolds are calculated.