Monogamy of correlations for broadcast copies of entangled states

By combining a measure of total correlations, mutual information, and the notion of broadcast-i.e. generally non-factorized-copies of states of distributed systems, we are able to characterize in a single framework different levels of quantumness of correlations, corresponding to the classification of strictly classical, separable, and entangled states. We find that the broadcast regularization of mutual information-defined as the minimal per-copy mutual information between parties, when they share an infinite amount of broadcast copies-besides having by construction an appealing interpretation, satisfies many of the properties of an entanglement measure. In particular, it vanishes for separable states while it is strictly positive for all entangled states. The latter fact may be considered a signature of monogamy of entangled correlations.