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arXiv · 2610.42017

Logical Bell Inequalities for Marginal Wigner Negativity

Sanchit Srivastava·Selman Ipek·Cihan Okay·Shohini Ghose
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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.

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Sanchit Srivastava, Selman Ipek, Cihan Okay, Shohini Ghose. 2026-10-30. Logical Bell Inequalities for Marginal Wigner Negativity. https://arxiv.org/abs/2610.42017

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