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Manifolds of interconvertible pure states

Magdalena M. Sinolecka·Karol Zyczkowski·Marek Kus
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Abstract

Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt decomposition. In particular, the generic orbit has 2N^2 -N-1 dimensions, the set of separable states is 4(N-1) dimensional, while the manifold of maximally entangled states has N^2-1 dimensions.

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Magdalena M. Sinolecka, Karol Zyczkowski, Marek Kus. 2001-11-14. Manifolds of interconvertible pure states. https://arxiv.org/abs/quant-ph/0110082

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