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

Given a bipartite quantum system represented by a Hilbert space H(1)xH(2), we give an elementary argument to show that if either dim H-1 = infinity or dim H-2 = infinity, then the set of nonseparable density operators on H(1)xH(2) is trace-norm dense in the set of all density operators land the separable density operators nowhere dense). This result complements recent detailed investigations of separability, which show that when dim H-i<infinity for i = 1,2, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.