Induced Bell-CHSH observables in the Fewster-Verch measurement scheme
Abstract
The Summers-Werner theorem shows that the vacuum of a relativistic quantum field theory violates the Bell-CHSH inequality maximally on complementary wedges, but it is an existence statement: it exhibits neither the observables nor an apparatus that measures them. We give an explicit operator-level realization within the Fewster-Verch measurement framework, obtaining dichotomic Bell observables of a free Majorana field in 1+1 dimensions as observables induced by local couplings to Majorana probes. The induced system smearing factorizes exactly as fh=k bλ,h, so its support is controlled by the compactly supported coupling profile k; dichotomy is imposed by calibrating and normalizing the induced smearings rather than required of the probe observable; and a probe-only normal ordering yields the product of Alice's and Bob's induced bilinears, which the non-multiplicative induced map alone does not provide. Under explicit attainability hypotheses the induced observables saturate the Tsirelson bound in a state prepared from the vacuum. The construction extends to coupled scalar fields.
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BibTeX
@misc{guimaraes2026induced,
title = {{Induced Bell-CHSH observables in the Fewster-Verch measurement scheme}},
author = {M. S. Guimaraes and I. Roditi and S. P. Sorella},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33773},
eprint = {2610.33773},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33773},
}
RIS
TY - UNPB
TI - Induced Bell-CHSH observables in the Fewster-Verch measurement scheme
AU - M. S. Guimaraes
AU - I. Roditi
AU - S. P. Sorella
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33773
UR - https://arxiv.org/abs/2610.33773
AB - The Summers-Werner theorem shows that the vacuum of a relativistic quantum field theory violates the Bell-CHSH inequality maximally on complementary wedges, but it is an existence statement: it exhibits neither the observables nor an apparatus that measures them. We give an explicit operator-level realization within the Fewster-Verch measurement framework, obtaining dichotomic Bell observables of a free Majorana field in 1+1 dimensions as observables induced by local couplings to Majorana probes. The induced system smearing factorizes exactly as f_h=k b_λ,h, so its support is controlled by the compactly supported coupling profile k; dichotomy is imposed by calibrating and normalizing the induced smearings rather than required of the probe observable; and a probe-only normal ordering yields the product of Alice's and Bob's induced bilinears, which the non-multiplicative induced map alone does not provide. Under explicit attainability hypotheses the induced observables saturate the Tsirelson bound in a state prepared from the vacuum. The construction extends to coupled scalar fields.
ER -