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arXiv · 0805.3134

Closed formula for the relative entropy of entanglement

Adam Miranowicz·Satoshi Ishizaka
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Abstract

The long-standing problem of finding a closed formula for the relative entropy of entanglement (REE) for two qubits is addressed. A compact-form solution to the inverse problem, which characterizes an entangled state for a given closest separable state, is obtained. Analysis of the formula for a large class of entangled states strongly suggests that a compact analytical solution of the original problem, which corresponds to finding the closest separable state for a given entangled state, can be given only in some special cases. A few applications of the compact-form formula are given to show additivity of the REE, to relate the REE with the Rains upper bound for distillable entanglement, and to show that a Bell state does not have a unique closest separable state.

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Adam Miranowicz, Satoshi Ishizaka. 2008-10-15. Closed formula for the relative entropy of entanglement. https://doi.org/10.1103/physreva.78.032310

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