We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored. In quantum information theory it is common to distinguish between purely classical information, measured in bits, and quantum information, which is measured in qubits. These differ in the channel resources required to communicate them. Qubits may not be sent by a classical channel alone, but must be sent either via a quantum channel which preserves coherence or by teleportation through an entangled channel with two classical bits of communication [1] . In this context, one qubit is equivalent to one unit of shared entanglement, or 'e-bit', together with two classical bits. Any bipartite quantum state may be used as a communication channel with some degree of success, and so it is of interest to determine how to separate the correlations it contains into a classical and an entangled part. A number of measures of entanglement and of total correlations have been proposed in recent years [2, 3, 4, 5, 6] . However, it is still not clear how to quantify the purely classical part of the total bipartite correlations. In this paper we propose a possible measure of classical correlations and investigate its properties. We first review the existing measures of entangled and total correlations. In classical information theory, the Shannon entropy, H(X) ≡ H(p) = − i p i log p i , is used to quantify the information in a source, X, that produces messages x i with probabilities p i [7, 8] . The relative entropy is a useful measure of the closeness of two probability distributions {p i } and {q i } from the same source X. The relative entropy of {p i } to {q i } is defined as H(p||q) = i p i log p i q i . Correlations between 1
In REF , some properties, especially the correlation between classical and quantum system has been studied.
Classical, quantum and total correlations
Physics