Bruno Bellomo, Rosario Lo Franco, Giuseppe Compagno
We introduce the notion of linear relative entropy as measure of distance between states of multipartite quantum systems. When the symmetric form of linear relative entropy, which remarkably coincides with the square norm distance measure, is used to measure the distance between the state of the system and its closest classical state it coincides with geometric quantum discord. This shows that the definitions of entropic (von Neumann) and geometric quantum discord are thus connected by a change of entropy measures. Generalized relative entropies are then introduced, von Neumann and linear relative entropies being particular cases. Linear relative entropy is used here for the first time to quantify also total and classical correlations. We then show that linear and von Neumann relative entropies, when used as measures of quantum discord in an open two-qubit system, present qualitatively different dynamical behaviors. Therefore they are not, in general, equivalent in describing the dynamics of quantum correlations. Moreover they exhibit, in the state space, qualitative differences even for total correlations. This aspect indicates that differences found for quantum discord are not attributable to a different separation, introduced by each measure, between quantum and classical parts of correlations.
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http://arxiv.org/abs/1104.4043
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