We give an operational definition of the quantum, classical, and total amounts 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 we have 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. As a by-product, we obtain a direct, operational, and elementary proof of strong subadditivity of quantum entropy.
|Translated title of the contribution||Quantum, classical, and total amount of correlations in a quantum state|
|Article number||Art No 032317|
|Journal||Physical Review A: Atomic, Molecular and Optical Physics|
|Publication status||Published - Sep 2005|
Bibliographical notePublisher: American Physical Society
Other identifier: IDS number 969IR