Information and quantum nonseparability

An information-theoretic inequality analogous to the well-known result of Bell [Physics 1, 195 (1964)] is formulated using the concept of information distance. This inequality, like Bell's, is true for all local-hidden-variable theories, but not for quantum mechanics. The metric space structure of this new inequality suggests a reformulation of familiar Bell inequalities in terms of a ``covariance distance.'' Quantum nonseparability can be demonstrated through violations of these inequalities even in cases where the correlation between two systems is extremely weak. The connection between nonseparability and complementarity is also briefly discussed in this paper.