Generic Bell correlation between arbitrary local algebras in quantum field theory

TL;DR

This paper demonstrates that in quantum field theory, Bell correlated states are densely present between local algebras, implying widespread entanglement across spacelike separated regions, with broad implications for quantum correlations.

Contribution

It proves the density of Bell correlated states for infinite type von Neumann algebras and applies this to quantum field theory, showing pervasive entanglement between spacelike regions.

Findings

Bell correlated states are norm dense for infinite type algebras.

Any vector cyclic for one algebra is entangled across the pair.

All bounded energy field states are entangled across spacelike regions.

Abstract

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.