Logical Bell Inequalities for Marginal Wigner Negativity

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.

Source: arXiv:2610.42017v1 - http://arxiv.org/abs/2610.42017v1 PDF: https://arxiv.org/pdf/2610.42017v1 Original Link: http://arxiv.org/abs/2610.42017v1