Geometry and Product States

Details Geometry and Product States Geometry and Product States

2000-10-03

arxiv.org/abs/quant-ph/0010013v1

Quantum Info. and Comp. Vol 2, #5, p. 333-347 (2002)

Physics

Quantum Physics

Scientific paper

As separable states are a convex combination of product states, the geometry of the manifold of product states is studied. Prior results by Sanpera, Vidal and Tarrach are extended. Furthermore, it is proven that states in the set tangent to the manifold of product states, at the maximally mixed state are separable; the set normal constains, among others, all maximally entangled states. A canonical decomposition is given. A surprising result is that for the case of two particles, the closest product state to the maximally entangled state is the maximally mixed state. An algorithm is provided to find the closest product state.

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