Generic Bell correlation between arbitrary local algebras in quantum field theory

Details Generic Bell correlation between arbitrary local algebras in quantum field theory Generic Bell correlation between arbitrary local algebras in quantum field theory

1999-09-12

arxiv.org/abs/math-ph/9909013v3

J.Math.Phys. 41 (2000) 1711-1717

Physics

Mathematical Physics

Third version; correction in the proof of Proposition 4

Scientific paper

10.1063/1.533253

We prove that for any two commuting von Neumann algebras of infinite type, the open set of Bell correlated states for the two algebras is norm dense. We then apply this result to algebraic quantum field theory -- where all local algebras are of infinite type -- in order to show that for any two spacelike separated regions, there is an open dense set of field states that dictate Bell correlations between the regions. We also show that any vector state cyclic for one of a pair of commuting nonabelian von Neumann algebras is entangled (i.e., nonseparable) across the algebras -- from which it follows that every field state with bounded energy is entangled across any two spacelike separated regions.

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