Bipartitemixedstates of infinitedimensional systems are generically nonseparable
Abstract
Given a bipartite quantum system represented by a Hilbert space H_{1}⊗H_{2}, we give an elementary argument to show that if either dim H_{1}=∞ or dim H_{2}=∞, then the set of nonseparable density operators on H_{1}⊗H_{2} is tracenorm 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 H_{i}<∞ 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:quantph/9908028
 Bibcode:
 1999PhRvA..61a2108C
 Keywords:

 03.65.Bz;
 Quantum Physics
 EPrint:
 5 pages, RevTeX