Given a bipartite quantum system represented by a Hilbert space H1⊗H2, we give an elementary argument to show that if either dim H1 = ∞ or dim H2 = ∞, then the set of nonseparable density operators on H1⊗H2 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 dim Hi<∝ for i = 1,2, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.
|Original language||English (US)|
|Number of pages||5|
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|State||Published - Jan 2000|
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics