Quantum Bayesian Networks: Compositionality and Typing via Linear Logic
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918524499263488 |
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| author | Di Guardia, Rémi Ehrhard, Thomas Faggian, Claudia |
| author_facet | Di Guardia, Rémi Ehrhard, Thomas Faggian, Claudia |
| contents | 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.
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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_26059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Bayesian Networks: Compositionality and Typing via Linear Logic Di Guardia, Rémi Ehrhard, Thomas Faggian, Claudia Logic in Computer Science 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. 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. |
| title | Quantum Bayesian Networks: Compositionality and Typing via Linear Logic |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2604.26059 |