Entanglement in Algebraic Quantum Field Theories

TL;DR

This paper explores the mathematical framework of Algebraic Quantum Field Theory (AQFT) for analyzing entanglement and Bell inequalities, extending the approach to curved spacetimes using category theory.

Contribution

It formulates AQFT using Haag-Araki-Kastler axioms and extends the algebraic entanglement approach to general spacetimes via locally covariant QFT.

Findings

Mathematical structures for AQFT are detailed.

Extension of entanglement and Bell inequalities to curved spacetimes.

Use of category theory for spacetime generalization.

Abstract

There has been some recent interest in applying the techniques of Algebraic Quantum Field Theory (AQFT) to entanglement problems in perturbative QFT. In particular, the Hilbert space independence of this formulation makes it particularly interesting in the context of curved spacetimes and the emphasis on the algebra of observables makes the treatment of Bell inequalities in QFT resemble such treatment in non-relativistic Quantum Mechanics. In this work, we present the mathematical structures needed for formulating AQFT in terms of the Haag-Araki-Kastler (HAK) axioms and discuss their implications. Moreover, we discuss the algebraic approach to quantum entanglement in the form of Bell inequalities. We provide an extension of this formulation to general globally hyperbolic spacetimes using the so-called Locally Covariant approach to QFT, which extends the HAK axioms to general spacetimes by means of the Category Theory language.