2026-07-19T20:47:34Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26366 2026-07-15T06:01:57Z ddc:004 open_access

Quantum Bayesian Networks: Compositionality and Typing via Linear Logic Di Guardia, Rémi Ehrhard, Thomas Faggian, Claudia Quantum Bayesian Networks Quantum Causal Models Bayesian Networks Proof-Nets Linear Logic Quantum Bayesian networks [Henson et al., 2014] provide a mathematical formalism to describe causal relations, to analyse correlations, and to predict the probabilities of measurement outcomes, in systems involving both classical and quantum data. They generalize Pearl’s Bayesian networks [Pearl, 2009] - prominent graphical models for classical probabilistic reasoning and inference. The goal of this paper is to bring compositional principles and a typing discipline into this setting. A key feature of our compositional semantics is that when all causes are classical, it coincides with the standard factor-based semantics of Bayesian networks, while in the purely quantum case it reduces to tensor networks. We then propose a typed formalism based on linear logic proof-nets, where types ensure well-behaved composition of systems, and which we prove sound and complete with respect to quantum Bayesian networks. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Rémi Di Guardia and Thomas Ehrhard and Claudia Faggian 2026 Is Part Of LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2026.16 urn:nbn:de:0030-drops-263668 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.16 eng https://creativecommons.org/licenses/by/4.0/legalcode