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

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.

Automated summary

In this paper, we propose 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. By constructing specific test functions and satisfying relativistic causality requirements, we report violations of the Bell-CHSH inequality as close as desired to Tsirelson's bound.