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arXiv:0806.1892 · Physical Review A

Quantum Chernoff bound as a measure of nonclassicality for one-mode Gaussian states

Mădălina Boca, Iulia Ghiu, Paulina Marian, Tudor A. Marian

Published Jan 20, 2009• 24 citations
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Abstract

We evaluate a Gaussian distance-type degree of nonclassicality for a single-mode Gaussian state of the quantum radiation field by use of the recently discovered quantum Chernoff bound. The general properties of the quantum Chernoff overlap and its relation to the Uhlmann fidelity are interestingly illustrated by our approach.
DOI
10.1103/physreva.79.014302

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We analyze the Uhlmann fidelity of a pair of nnn-mode Gaussian states of the quantum radiation field. This quantity is shown to be the product of an exponential function depending on the relative average displacement and a factor fully determined by the symplectic spectrum of the covariance matrix of a specific Gaussian state. However, it is difficult to handle our general formula unless the Gaussian states commute or at least one of them is pure. On the contrary, in the simplest cases n=1n=1n=1 and n=2n=2n=2, it leads to explicit analytic formulas. Our main result is a calculable expression of the fidelity of two arbitrary two-mode Gaussian states. This can be applied to build reliable measures of quantum correlations between modes in various branches of quantum physics.
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We introduce and investigate a distance-type measure of non-Gaussianity based on the quantum fidelity. This new measure can readily be evaluated for all pure states and the mixed ones that are diagonal in the Fock basis. In particular, for an M -photon-added thermal state, an analysis of the Bures degree of non-Gaussianity is performed in comparison with two previous measures built with the Hilbert–Schmidt metric and the relative entropy. We obtain a compact analytic formula for the Hilbert–Schmidt measure of non-Gaussianity and find good consistency between the three examined measures.