On the quantum, classical and total amount of correlations in a quantum state
Abstract
We give an operational definition of the quantum, classical and total amount of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation one has to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation for the first time. As a byproduct, we obtain a direct, operational and elementary proof of strong subadditivity of quantum entropy.
Cite
@article{arxiv.quant-ph/0410091,
title = {On the quantum, classical and total amount of correlations in a quantum state},
author = {Berry Groisman and Sandu Popescu and Andreas Winter},
journal= {arXiv preprint arXiv:quant-ph/0410091},
year = {2007}
}
Comments
12 pages ReVTeX4, 2 eps figures. v2 has some arguments clarified and references updated