Locking Classical Correlations in Quantum States

We show that there exist bipartite quantum states which contain a large locked classical correlation that is unlocked by a disproportionately small amount of classical communication. In particular, there are $(2n+1)$-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from $n/2$ bits to $n$ bits. This phenomenon is impossible classically. However, states exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.