Bounding Classical and Quantum Correlations in Bayesian Networks with Quasiprobabilities
Abstract
Bell's theorem reveals that quantum theory is in tension with classical causal reasoning and, in particular, the notion of local causality. This is now understood as a particular example of non-classicality in the study of correlations in (Bayesian) networks with both unobserved and observed nodes: the correlations are probability distributions over the observed nodes. There is a great deal of work aiming to understand the bounds on quantum and classical correlations in such networks and one approach is to consider outer approximations to the former. Along these lines, we consider quasiprobabilistic models for Bayesian networks, which can be seen as classical models but the probability distributions involving unobserved nodes are "replaced" with quasiprobabilities that respect normalisation but not positivity. We denote the set of correlations resulting from these models as the quasi set. Such models have a history in the study of Bell-type non-classicality where it has been shown that they can produce all non-signalling correlations. We show a generalisation of this result for a broad class of networks, which motivates a conjecture that the quasi set recovers the so called nested Markov model. Our work utilises a connection to tensor network decompositions, which may be of independent interest.
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BibTeX
@misc{becsi2026bounding,
title = {{Bounding Classical and Quantum Correlations in Bayesian Networks with Quasiprobabilities}},
author = {Paul Becsi and Matty J. Hoban},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.23372},
eprint = {2606.23372},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.23372},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bounding Classical and Quantum Correlations in Bayesian Networks with Quasiprobabilities
AU - Paul Becsi
AU - Matty J. Hoban
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2606.23372
UR - https://arxiv.org/abs/2606.23372
AB - Bell's theorem reveals that quantum theory is in tension with classical causal reasoning and, in particular, the notion of local causality. This is now understood as a particular example of non-classicality in the study of correlations in (Bayesian) networks with both unobserved and observed nodes: the correlations are probability distributions over the observed nodes. There is a great deal of work aiming to understand the bounds on quantum and classical correlations in such networks and one approach is to consider outer approximations to the former. Along these lines, we consider quasiprobabilistic models for Bayesian networks, which can be seen as classical models but the probability distributions involving unobserved nodes are "replaced" with quasiprobabilities that respect normalisation but not positivity. We denote the set of correlations resulting from these models as the quasi set. Such models have a history in the study of Bell-type non-classicality where it has been shown that they can produce all non-signalling correlations. We show a generalisation of this result for a broad class of networks, which motivates a conjecture that the quasi set recovers the so called nested Markov model. Our work utilises a connection to tensor network decompositions, which may be of independent interest.
ER -