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.
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BibTeX
@misc{srivastava2026logical,
title = {{Logical Bell Inequalities for Marginal Wigner Negativity}},
author = {Sanchit Srivastava and Selman Ipek and Cihan Okay and Shohini Ghose},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42017},
eprint = {2610.42017},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42017},
}
RIS
TY - UNPB
TI - Logical Bell Inequalities for Marginal Wigner Negativity
AU - Sanchit Srivastava
AU - Selman Ipek
AU - Cihan Okay
AU - Shohini Ghose
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42017
UR - https://arxiv.org/abs/2610.42017
AB - 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.
ER -