1999/09/30 by Hans Halvorson, Rob Clifton · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Quantum Information and Cryptography #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1063/1.533253
published as J.Math.Phys. 41 (2000) 1711-1717 · Third version; correction in the proof of Proposition 4
arxiv created 2000/01/08 · openalex publication_date 2000/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.