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

Rob Clifton, Hans Halvorson

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

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.

Original languageEnglish (US)
Article number012108
Pages (from-to)121081-121085
Number of pages5
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume61
Issue number1
StatePublished - Jan 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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