Bipartite-mixed-states of infinite-dimensional systems are generically nonseparable

Given a bipartite quantum system represented by a Hilbert space [Formula Presented] we give an elementary argument to show that if either [Formula Presented] or [Formula Presented] then the set of nonseparable density operators on [Formula Presented] is trace-norm dense in the set of all density operators (and the separable density operators nowhere dense). This result complements recent detailed investigations of separability, which show that when [Formula Presented] for [Formula Presented] there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.