Covariance, correlation and entanglement

Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based upon covariance. This works for two-and three-component systems but produces ambiguities for multicomponent systems of composite dimension. Its relationship to angular momentum dispersion for symmetric spin states is described.