Logical Bell Inequalities for Marginal Wigner Negativity

Abstract:We construct logical Bell inequalities whose violations are determined by the Wigner function of a reduced quantum state. For odd-prime qudits, each phase-space point of any nonempty proper subsystem defines an inequality, violated precisely when the corresponding Gross Wigner value is negative. This correspondence allows us to quantify the contextuality that a reduced state guarantees for the composite system. The normalized violation gives a lower bound on the contextual fraction in the complete Weyl measurement scenario, valid for every joint state with that marginal, irrespective of its correlations. We identify a family of product states that saturates this bound. For these states, one marginal Wigner value fixes the contextual fraction of the entire system.

arXiv:2610.42017 [quant-ph]

(or arXiv:2610.42017v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.42017 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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