Classical, quantum and total correlations

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