  A general framework is developed for separating classical and quantum
correlations in a multipartite system. Entanglement is defined as the
difference in the correlation information encoded by the state of a system and
a suitably defined separable state with the same marginals. A generalization of
the Schmidt decomposition is developed to implement the separation of
correlations for any pure, multipartite state. The measure based on this
decomposition is a generalization of the entanglement of formation to
multipartite systems, provides an upper bound for the relative entropy of
entanglement, and is directly computable on pure states. The example of pure
three-qubit states is analyzed in detail, and a classification based on
minimal, four-term decompositions is developed.
