Generic Bell correlation between arbitrary local algebras in quantum field theory
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Generic Bell correlation between arbitrary local algebras in quantum field theory. / Halvorson, Hans; Clifton, Rob.
I: Journal of Mathematical Physics, Bind 41, Nr. 4, 2000, s. 1711-1717.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Generic Bell correlation between arbitrary local algebras in quantum field theory
AU - Halvorson, Hans
AU - Clifton, Rob
PY - 2000
Y1 - 2000
N2 - 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.
AB - 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.
U2 - 10.1063/1.533253
DO - 10.1063/1.533253
M3 - Journal article
AN - SCOPUS:0034347145
VL - 41
SP - 1711
EP - 1717
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 4
ER -
ID: 289119347