Bipartite-mixed-states of infinite-dimensional systems are generically nonseparable - art. no. 012108

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 sepa rable density operators nowhere dense). This result complements recent deta iled investigations of separability, which show that when dim H-i<infinity for i = 1,2, there is a separable neighborhood (perhaps very small for larg e dimensions) of the maximally mixed state.