Polyteam logics for quantum contextuality
Abstract
We introduce logics of dependence and independence over polyteams (that is, databases with multiple relation schemes), in a similar way as in arXiv:1704.02158v3 [cs.LO]. On this basis, we develop a logical framework in which we can express (in formulas) relevant properties about the statistics of a repeated quantum experiment. In this framework, we formalize Bell's theorem, and the Kochen-Specker theorem as failure of logical entailments, as it was suggested in arXiv:2107.10817v3 [math.LO]. The key feature of polyteam logics in action here is their power to express both local and global properties, with respect to the set of possible measurements. The point of this is at least twofold. Firstly, as in arXiv:1102.0264v7 [quant-ph], it gives a high-level (information-theoretic) understanding of these physical phenomena, that is not intrinsic to the physical objects involved. Secondly, since logical entailment is often (partially) axiomatizable, this framework incites us to tackle the question of contextuality computationally. We also define semiring-weighted polyteams along with logics on them, and use them to recover the probabilistic versions of the contextuality theorems mentioned above.
Related
- Classical and Quantum Logics with Multiple Non-Equivalent and Non-Isomorphic Models
- Simultaneous extensions of states on quantum logics
- Chromatic Constraints on Quantum Observables: Gaps, Contextuality, and Separability
- Structural Realizations and Invariants of Universal Obstruction Cohomology: Goodwillie Towers, Chromatic Filtrations, and Quantum Contextuality
- Logics of Filter Bubbles
BibTeX
@misc{maguet2026polyteam,
title = {{Polyteam logics for quantum contextuality}},
author = {Loan Le Maguet},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00814},
eprint = {2611.00814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00814},
}
RIS
TY - UNPB
TI - Polyteam logics for quantum contextuality
AU - Loan Le Maguet
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00814
UR - https://arxiv.org/abs/2611.00814
AB - We introduce logics of dependence and independence over polyteams (that is, databases with multiple relation schemes), in a similar way as in arXiv:1704.02158v3 [cs.LO]. On this basis, we develop a logical framework in which we can express (in formulas) relevant properties about the statistics of a repeated quantum experiment. In this framework, we formalize Bell's theorem, and the Kochen-Specker theorem as failure of logical entailments, as it was suggested in arXiv:2107.10817v3 [math.LO]. The key feature of polyteam logics in action here is their power to express both local and global properties, with respect to the set of possible measurements. The point of this is at least twofold. Firstly, as in arXiv:1102.0264v7 [quant-ph], it gives a high-level (information-theoretic) understanding of these physical phenomena, that is not intrinsic to the physical objects involved. Secondly, since logical entailment is often (partially) axiomatizable, this framework incites us to tackle the question of contextuality computationally. We also define semiring-weighted polyteams along with logics on them, and use them to recover the probabilistic versions of the contextuality theorems mentioned above.
ER -