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 into a quantum part and a classical part thanks to an additive relation involving only the distances between states. Here we investigate a unified view of correlations using as a distance measure the square norm, which has already been used to define the so-called geometric quantum discord. We thus also consider geometric quantifiers 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 no longer satisfy a closed additivity relation.

Bellomo, B., Giorgi, G.L., Galve, F., Lo Franco, R., Compagno, G., Zambrini, R. (2012). Unified view of correlations using the square-norm distance. PHYSICAL REVIEW A, 85(3), 032104-1-032104-9 [10.1103/PhysRevA.85.032104].

Unified view of correlations using the square-norm distance

BELLOMO, Bruno;LO FRANCO, Rosario;COMPAGNO, Giuseppe;
2012-01-01

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 into a quantum part and a classical part thanks to an additive relation involving only the distances between states. Here we investigate a unified view of correlations using as a distance measure the square norm, which has already been used to define the so-called geometric quantum discord. We thus also consider geometric quantifiers 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 no longer satisfy a closed additivity relation.
2012
Settore FIS/03 - Fisica Della Materia
Bellomo, B., Giorgi, G.L., Galve, F., Lo Franco, R., Compagno, G., Zambrini, R. (2012). Unified view of correlations using the square-norm distance. PHYSICAL REVIEW A, 85(3), 032104-1-032104-9 [10.1103/PhysRevA.85.032104].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/66624
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