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

Rob Clifton; Hans Halvorson

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

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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 H_i<∝ for i = 1,2, there is a separable neighborhood (perhaps very small for large dimensions) of the maximally mixed state.

Original language	English (US)
Article number	012108
Pages (from-to)	121081-121085
Number of pages	5
Journal	Physical Review A - Atomic, Molecular, and Optical Physics
Volume	61
Issue number	1
State	Published - Jan 2000
Externally published	Yes

All Science Journal Classification (ASJC) codes

Atomic and Molecular Physics, and Optics

Cite this

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title = "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.",

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AU - Clifton, Rob

AU - Halvorson, Hans

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N2 - 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.

AB - 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.

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JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 1

M1 - 012108

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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