Closed formula for the relative entropy of entanglement in all dimensions

Details Closed formula for the relative entropy of entanglement in all dimensions Closed formula for the relative entropy of entanglement in all dimensions

2010-07-26

arxiv.org/abs/1007.4544v2

J. Math. Phys. 52, 052201 (2011)

Physics

Quantum Physics

8 pages, 1 figure, significantly revised; theorem 1 is now providing necessary and sufficient conditions to determine if a sta

Scientific paper

10.1063/1.3591132

The relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state (CSS). Given a multipartite-state on the boundary of the set of separable states, we find a closed formula for all the entangled state for which this state is a CSS. Quite amazing, our formula holds for multipartite states in all dimensions. In addition we show that if an entangled state is full rank, then its CSS is unique. For the bipartite case of two qubits our formula reduce to the one given in Phys. Rev. A 78, 032310 (2008).

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