Quantum Relative Entropy - An Entanglement Measure

An Entanglement Measure

Let a composite quantum system have state space

and ρ be a density matrix acting on H.

The relative entropy of entanglement of ρ is defined by

where the minimum is taken over the family of separable states. A physical interpretation of the quantity is the optimal distinguishability of the state ρ from separable states.

Clearly, when ρ is not entangled

by Klein's inequality.

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