Bell’s inequalities and quantum field theory

Miklós Rédei

Gábor Hofer‐Szabó, Péter Vecsernyés

Miklós Rédei

Stephen J. Summers, Reinhard F. Werner

Grossi, Rafael, J. C. A. Barata

We propose a generalization of the description of Bell's inequalities in algebraic quantum field theory (AQFT) to the context of locally covariant quantum field theory (LCQFT). We use the functorial formulation of the state space as proposed in the seminal work \cite{BFV03} to show that for the suitable subcategory which consists of all possible admissible quadruples, yields a category of states over such observables which satisfy the Clauser-Horne-Shimony-Holt (CHSH) inequality. Such inequality is trivially preserved under algebraic morphisms and functoriality of the state space asserts us that it is preserved under isometric embeddings between the globally hyperbolic spacetimes where the algebras are defined and which constitute the locally covariant QFT functor.

Stephen J. Summers, Reinhard F. Werner

In the context of the study of Bell’s inequalities carried out in Paper I [J. Math. Phys. 28, 2440 (1987)], it is proven that Bell’s inequalities are maximally violated in the vacuum state by suitable spacelike separated observables for both Bose and Fermi free quantum field theories.