Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable

Details Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable

1999-08-08

arxiv.org/abs/quant-ph/9908028v1

Phys. Rev. A 61, 012108 (2000)

Physics

Quantum Physics

5 pages, RevTeX

Scientific paper

10.1103/PhysRevA.61.012108

Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators 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 both component Hilbert spaces are finite-dimensional, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.

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