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.

We consider how much entanglement can be produced by a nonlocal two-qubit unitary operation, U AB -the entangling capacity of U AB . For a single application of U AB , with no ancillas, we find the entangling capacity and show that it generally helps to act with U AB on an entangled state. Allowing ancillas, we present numerical results from which we can conclude, quite generally, that allowing initial entanglement typically increases the optimal capacity in this case as well. Next, we show that allowing collective processing does not increase the entangling capacity if initial entanglement is allowed.

Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is shown to depend on the availability of classical information about particular members of the ensemble. Based on this, relations between relative entropy of entanglement and mutual information are derived.In quantifying entanglement, a number of measures have been proposed. For bipartite pure states, ρ AB , the Von Neumann entropy of the reduced density matrix of either subsystem, ρ A or ρ B , has been found to be a good and unique measure, [1], [2]. Relative entropy of entanglement has been proposed as a measure which extends to mixed states, [3], [4]. Loosely speaking, it quantifies how 'far' an entangled state is from the set of disentangled states. Entanglement of mixed states has also been characterised by the 'entanglement of formation', [5], [6], and by the 'entanglement of distillation', [5]. Rather surprisingly, use of entanglement in mixed states is not reversible in the sense that all the entanglement required to construct a particular mixed state cannot be distilled out again, so the entanglement of formation is greater than the entanglement of distillation, [4]. In this paper, we clarify the role of classical information about the identity of particular members of an ensemble of mixed states, and show that the loss of such information is responsible for the difference between the entanglement of formation and the entanglement of distillation. We provide a unifying frame-work for entanglement measures by showing how previously proposed measures are special cases of the relative entropy of entanglement. This gives a strong 1

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