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arXiv · 1112.6370

Unified view of correlations using the square norm distance

Bruno Bellomo·Gian Luca Giorgi·Fernando Galve·Rosario Lo Franco·Giuseppe Compagno·Roberta Zambrini
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Abstract

The distance between a quantum state and its closest state not having a certain property has been used to quantify the amount of correlations corresponding to that property. This approach allows a unified view of the various kinds of correlations present in a quantum system. In particular, using relative entropy as a distance measure, total correlations can be meaningfully separated in a quantum and a classical part thanks to an additive relation involving only distances between states. Here, we investigate a unified view of correlations using as distance measure the square norm, already used to define the so-called geometric quantum discord. We thus consider geometric quantifiers also for total and classical correlations finding, for a quite general class of bipartite states, their explicit expressions. We analyze the relationship among geometric total, quantum and classical correlations and we find that they do not satisfy anymore a closed additivity relation.

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Bruno Bellomo, Gian Luca Giorgi, Fernando Galve, Rosario Lo Franco, Giuseppe Compagno, Roberta Zambrini. 2012-03-05. Unified view of correlations using the square norm distance. https://doi.org/10.1103/physreva.85.032104

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