Relative entropy is an exact measure of non-Gaussianity

Abstract

We prove that the closest Gaussian state to an arbitrary $N$-mode field state through the relative entropy is built with the covariance matrix and the average displacement of the given state. Consequently, the relative entropy of an $N$-mode state to its associate Gaussian one is an exact distance-type measure of non-Gaussianity. In order to illustrate this finding, we discuss the general properties of the $N$-mode Fock-diagonal states and evaluate their exact entropic amount of non-Gaussianity.

6 pages, no figures. Comments are welcome

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• Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
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