Communications in Mathematical Physics

Maximal violation of Bell's inequalities is generic in quantum field theory

Stephen J. Summers, Reinhard F. Werner

Published Jun 1, 1987• 191 citations

Publisher

DOI: 10.1007/bf01207366

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Communications in Mathematical Physics

Maximal violation of Bell's inequalities is generic in quantum field theory

Stephen J. Summers, Reinhard F. Werner

Published Jun 1, 1987• 191 citations

Publisher

DOI: 10.1007/bf01207366

Related papers

Violation of Bell’s inequality in quantum field theory

Miklós Rédei

Springer eBooksJan 1, 19980 citations

Bell’s inequalities and quantum field theory. II. Bell’s inequalities are maximally violated in the vacuum

Stephen J. Summers, Reinhard F. Werner

Journal of Mathematical PhysicsOct 1, 1987144 citations

Maximal violation of the Bell-Clauser-Horne-Shimony-Holt inequality via bumpified Haar wavelets

David Dudal, Philipe De Fabritiis, M. S. Guimarães +2 more

We devise a general setup to investigate the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality in the vacuum state in the context of quantum field theory. We test the method with massless spinor fields in ( $1+1$ )-dimensional Minkowski space-time. Alice's and Bob's test functions are explicitly constructed, first by employing Haar wavelets which are then bumpified into proper test functions via a smoothening procedure relying on the Planck-taper window function. Relativistic causality is implemented by requiring the support of Alice's and Bob's test functions to be located in the left and right Rindler wedges, respectively. Violations of the Bell-CHSH inequality as close as desired to Tsirelson's bound are reported. We briefly comment on the extra portal, compared to earlier works; this opens the opportunity to scrutinize Bell-CHSH inequalities with generic, interacting quantum field theories.We devise a general setup to investigate the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality in the vacuum state in the context of quantum field theory. We test the method with massless spinor fields in ($1+1$)-dimensional Minkowski space-time. Alice's and Bob's test functions are explicitly constructed, first by employing Haar wavelets which are then bumpified into proper test functions via a smoothening procedure relying on the Planck-taper window function. Relativistic causality is implemented by requiring the support of Alice's and Bob's test functions to be located in the left and right Rindler wedges, respectively. Violations of the Bell-CHSH inequality as close as desired to Tsirelson's bound are reported. We briefly comment on the extra portal, compared to earlier works; this opens the opportunity to scrutinize Bell-CHSH inequalities with generic, interacting quantum field theories.

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Physics Letters AFeb 1, 1987232 citations

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Jan Hamhalter, Ekaterina Aleksandrovna Turilova

We formulate and prove Bell’s inequalities in the realm of JB $^*$ triples and JB $^*$ algebras. We show that the maximal violation of Bell’s inequalities occurs in any JBW $^*$ triple containing a nonassociative $2$ -Peirce subspace. Moreover, we show that the violation of Bell’s inequalities in a nonmodular JBW $^*$ algebra and in an essentially nonmodular JBW $^*$ triple is generic. We describe the structure of maximal violators and its relation to the spin factor. In addition, we present a synthesis of available results based on a unified geometric approach.We formulate and prove Bell’s inequalities in the realm of JB $$^*$$ triples and JB $$^*$$ algebras. We show that the maximal violation of Bell’s inequalities occurs in any JBW $$^*$$ triple containing a nonassociative $$2$$ -Peirce subspace. Moreover, we show that the violation of Bell’s inequalities in a nonmodular JBW $$^*$$ algebra and in an essentially nonmodular JBW $$^*$$ triple is generic. We describe the structure of maximal violators and its relation to the spin factor. In addition, we present a synthesis of available results based on a unified geometric approach.

Proceedings of the Steklov Institute of MathematicsMar 1, 20240 citations

1+1

)-dimensional Minkowski space-time. Alice's and Bob's test functions are explicitly constructed, first by employing Haar wavelets which are then bumpified into proper test functions via a smoothening procedure relying on the Planck-taper window function. Relativistic causality is implemented by requiring the support of Alice's and Bob's test functions to be located in the left and right Rindler wedges, respectively. Violations of the Bell-CHSH inequality as close as desired to Tsirelson's bound are reported. We briefly comment on the extra portal, compared to earlier works; this opens the opportunity to scrutinize Bell-CHSH inequalities with generic, interacting quantum field theories.

We formulate and prove Bell’s inequalities in the realm of JB

^*

triples and JB

^*

algebras. We show that the maximal violation of Bell’s inequalities occurs in any JBW

^*

triple containing a nonassociative

2

-Peirce subspace. Moreover, we show that the violation of Bell’s inequalities in a nonmodular JBW

^*

algebra and in an essentially nonmodular JBW

^*

triple is generic. We describe the structure of maximal violators and its relation to the spin factor. In addition, we present a synthesis of available results based on a unified geometric approach.