Bipartite-mixed-states of infinite-dimensional systems are generically nonseparable
Abstract
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.
- Publication:
-
Physical Review A
- Pub Date:
- December 1999
- DOI:
- 10.1103/PhysRevA.61.012108
- arXiv:
- arXiv:quant-ph/9908028
- Bibcode:
- 1999PhRvA..61a2108C
- Keywords:
-
- 03.65.Bz;
- Quantum Physics
- E-Print:
- 5 pages, RevTeX