Counterfactual entanglement and nonlocal correlations in separable states

It is shown that the outcomes of measurements on systems in separable mixed states can be partitioned, via subsequent measurements on a disentangled extraneous system, into subensembles that display the statistics of entangled states. This motivates the introduction of the concept of ``counterfactual'' entanglement, which can be associated with all separable mixed states, including those that are factorable. This type of entanglement gives rise to a kind of postselection-induced Bell inequality violation. The significance of counterfactual entanglement, and its physical implications, are assessed.