2000/10/03 by Robert B. Lockhart, Michael J. Steiner, Karl Gerlach
Physics and Astronomy · #quant-ph
published as Quantum Info. and Comp. Vol 2, #5, p. 333-347 (2002)
arxiv created 2000/10/03 · arxiv updated 2009/12/01
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.