Generic Bell correlation between arbitrary local algebras in quantum field theory

Hans Halvorson, Rob Clifton

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


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 non-Abelian 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.

Original languageEnglish (US)
Pages (from-to)1711-1717
Number of pages7
JournalJournal of Mathematical Physics
Issue number4
StatePublished - Apr 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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