Geometry of entangled states

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  • 14 June 2000
Abstract
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem. In particular we analyze the simplest case of 2 x 2 problem finding a stratification of the 6-D set of N=4 pure states. The set of effectively different states (which cannot be related by local transformations) is one dimensional. It starts at a 3-D manifold of maximally entangled states, cuts generic 5-D manifolds of entangled states (labeled by non-zero values of the entropy of entanglement), and ends at a single 4-D manifold of separable states.

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