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 \(\sqrt2\), 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.

arXiv:2610.03726 [quant-ph]

(or arXiv:2610.03726v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.03726 Focus to learn more arXiv-issued DOI via DataCite

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