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

TL;DR

This paper presents a method to demonstrate maximal violation of the Bell-CHSH inequality using bumpified Haar wavelets in quantum field theory, highlighting potential for analyzing interacting quantum fields.

Contribution

It introduces a novel approach employing bumpified Haar wavelets for Bell inequality tests in quantum field theory, enabling near Tsirelson's bound violations with relativistic causality.

Findings

Violations close to Tsirelson's bound achieved

Method applicable to massless spinor fields in 1+1 dimensions

Opens new avenues for studying Bell inequalities in interacting QFTs

Abstract

We devise a general setup to investigate the violation of the 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 to scrutinize Bell-CHSH inequalities with generic, interacting Quantum Field Theories.