Closed formula for the relative entropy of entanglement

Asymptotic relative entropy of entanglement.

We present an analytical formula for the asymptotic relative entropy of entanglement with respect to positive partial transpose states for Werner states of arbitrary dimension. We then demonstrate its validity using methods from convex optimization. This is the first case in which the asymptotic value of a subadditive entanglement measure has been calculated.

Gaussian relative entropy of entanglement

For two gaussian states with given correlation matrices, in order that relative entropy between them is practically calculable, I in this paper describe the ways of transforming the correlation matrix to matrix in the exponential density operator. Gaussian relative entropy of entanglement is proposed as the minimal relative entropy of the gaussian state with respect to separable gaussian state ...

Fisher - Hartwig Formula and Entanglement entropy

Toeplitz matrices have applications to different problems of statistical mechanics. Recently it was used for calculation of entanglement entropy in spin chains. In the paper we review these recent developments. We use Fisher-Hartwig formula, as well as the recent results concerning the asymp-totics of the block Toeplitz determinants, to calculate entanglement entropy of large block of spins in ...

Nodal-line entanglement entropy: Generalized Widom formula from entanglement Hamiltonians

Information, relative entropy of entanglement, and irreversibility.

Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is shown to depend on the availability of classical information about particular members of the ensemble. Based on this, relations between relative entropy of e...