The uniqueness theorem for entanglement measures
نویسندگان
چکیده
We review the mathematics of the theory of entanglement measures. As well as giving proofs from first principles for some well-known and important results, we provide a sharpened version of a uniqueness theorem which gives necessary and sufficient conditions for an entanglement measure to coincide with the reduced von Neumann entropy on pure states. We also prove several versions of a theorem on extreme entanglement measures in the case of mixed states. We analyse properties of the asymptotic regularization of entanglement measures proving, for example, convexity for the entanglement cost and for the regularized relative entropy of entanglement.
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