{"paper":{"title":"Quantum Bayesian Networks: Compositionality and Typing via Linear Logic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Quantum Bayesian networks receive a compositional semantics and linear-logic typing that reduces to standard Bayesian networks for classical data and to tensor networks for quantum data.","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Claudia Faggian, R\\'emi Di Guardia, Thomas Ehrhard","submitted_at":"2026-04-28T18:55:47Z","abstract_excerpt":"Quantum Bayesian networks 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 -- prominent graphical models for classical probabilistic reasoning and inference.\n  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 Bay"},"claims":{"count":3,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the proposed linear-logic typing and compositional semantics correctly capture all causal relations and measurement probabilities in mixed classical-quantum systems without requiring extra constraints or losing expressiveness.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quantum Bayesian networks receive a compositional semantics and linear-logic typing that reduces to standard Bayesian networks for classical data and to tensor networks for quantum data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"}],"snapshot_sha256":"5185bfdfb73c919b31fcee94293147777c429b7073cd1aeaacd3384ce825ffc6"},"source":{"id":"2604.26059","kind":"arxiv","version":2},"verdict":{"id":"3bc775bc-05be-4c0b-af92-c90eb0205b68","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:20:20.711944Z","strongest_claim":"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.","one_line_summary":"Quantum Bayesian networks receive a compositional semantics and linear-logic typing that reduces to standard Bayesian networks for classical data and to tensor networks for quantum data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the proposed linear-logic typing and compositional semantics correctly capture all causal relations and measurement probabilities in mixed classical-quantum systems without requiring extra constraints or losing expressiveness.","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26059/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T03:36:15.901935Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"da506898cd92b1ceec8b1dbce8c2969d40b262f2eaf7c297f7e06fa4f4bbe90c"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}