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

Given a bipartite quantum system represented by a Hilbert space H₁H₂, we give an elementary argument to show that if either dimH₁=∞ or dimH₂=∞, then the set of nonseparable density operators on H₁H₂ 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 dimHᵢ<∞ for $i=1,2,$ there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.