Minimum Experimental Information for Certifying Bell Nonlocality of Gravity
Abstract
A Bell violation by material probes certifies nonlocal behavior, but it does not identify which internal subsystem carried or was measured to produce that behavior. We determine the additional information required to attribute such a violation to a gravitational field. For any setting-independent field-to-probe channel completed before the Bell settings are chosen, an entanglement-breaking channel makes all induced field measurements jointly measurable. A static Newtonian phase pickup belongs to this class, even with arbitrary adaptive probe control. Applied to a recent four-mass proposal, the claimed field-only measurements obey the stronger CHSH bound √2, whereas the Bell-active operation is the source-to-probe instrument that includes the coherent source herald. At the published parameters, the observed flagged behavior is at least 0.1630 from the claimed field-detector family, exceeding its 0.0898 distance from Bell locality. We then incorporate a common field slice, gravitational constraints, dressing, detector backreaction, and coherent references into a robust certification theorem. The result isolates the minimum missing information: field-only factorization and a local measurement- incompatibility witness on each wing. More precise phase data cannot replace either requirement.
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BibTeX
@misc{sheng2026minimum,
title = {{Minimum Experimental Information for Certifying Bell Nonlocality of Gravity}},
author = {Jianqi Sheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03726},
eprint = {2610.03726},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03726},
}
RIS
TY - UNPB
TI - Minimum Experimental Information for Certifying Bell Nonlocality of Gravity
AU - Jianqi Sheng
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.03726
UR - https://arxiv.org/abs/2610.03726
AB - A Bell violation by material probes certifies nonlocal behavior, but it does not identify which internal subsystem carried or was measured to produce that behavior. We determine the additional information required to attribute such a violation to a gravitational field. For any setting-independent field-to-probe channel completed before the Bell settings are chosen, an entanglement-breaking channel makes all induced field measurements jointly measurable. A static Newtonian phase pickup belongs to this class, even with arbitrary adaptive probe control. Applied to a recent four-mass proposal, the claimed field-only measurements obey the stronger CHSH bound √2, whereas the Bell-active operation is the source-to-probe instrument that includes the coherent source herald. At the published parameters, the observed flagged behavior is at least 0.1630 from the claimed field-detector family, exceeding its 0.0898 distance from Bell locality. We then incorporate a common field slice, gravitational constraints, dressing, detector backreaction, and coherent references into a robust certification theorem. The result isolates the minimum missing information: field-only factorization and a local measurement- incompatibility witness on each wing. More precise phase data cannot replace either requirement.
ER -