Dimensions of generic local orbits of multipartite quantum systems

Details Dimensions of generic local orbits of multipartite quantum systems Dimensions of generic local orbits of multipartite quantum systems

2006-08-15

arxiv.org/abs/quant-ph/0608124v2

Physics

Quantum Physics

5 pages. The spelling of author's name corrected

Scientific paper

We consider the action of the group of local unitary transformations, U(m) x U(n), on the set of (mixed) states W of the bipartite m x n quantum system. We prove that the generic U(m) x U(n)--orbits in W have dimension m^2+n^2-2. This problem was mentioned (and left open) by Kus and Zyczkowski in their paper Geometry of entangled states. The proof can be extended to the case of arbitrary finite-dimensional multipartite quantum systems.

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