Modular wedge localization, Majorana fields and the Tsirelson limit of the Bell-CHSH inequality
J. G. A. Caribé, M. S. Guimaraes, I. Roditi, S. P. Sorella
TLDR
This paper investigates Bell-CHSH inequality violation in relativistic QFT using Majorana fields, showing it approaches the Tsirelson bound.
Key contributions
- Investigates Bell-CHSH inequality violation in relativistic QFT using massive Majorana fields in 1+1D.
- Provides a rapidity-space realization of Summers-Werner modular-localization construction.
- Reduces the vacuum Bell-CHSH correlator to a single spectral weight h²(ω) for the modular operator.
- Demonstrates approach to Tsirelson bound in vacuum state as spectral weight concentrates near ω≈0.
Why it matters
This work advances our understanding of quantum entanglement in relativistic quantum field theory. By showing how the Bell-CHSH inequality approaches the Tsirelson bound, it offers new insights into the fundamental limits of non-locality in quantum systems.
Original Abstract
The massive Majorana field in $1+1$ dimension is employed to investigate the violation of the Bell-CHSH inequality in relativistic Quantum Field Theory. We give an explicit rapidity-space realization of the Summers-Werner modular-localization construction and reduce the vacuum Bell-CHSH correlator to a single spectral weight $h^2(ω)$ for the modular operator. The resulting analytic families approach the Tsirelson bound in the vacuum state as their spectral weight concentrates near $ω\approx0$, corresponding to the eigenvalue $λ^2 \approx 1$ of the modular operator.
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