A Logical Basis for Quantum Evolution and Entanglement

Abstract : We reconsider discrete quantum causal dynamics where quan-tum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges de-pict propagation between events. Evolution is described as happening between a special family of spacelike slices, which were referred to as locative slices. Such slices are not so large as to result in acausal influ-ences, but large enough to capture nonlocal correlations. In our logical interpretation, edges are assigned logical formulas in a spe-cial logical system, called BV, an instance of a deep inference system. We demonstrate that BV, with its mix of commutative and noncommutative connectives, is precisely the right logic for such analysis. We show that the commutative tensor encodes (possible) entanglement, and the non-commutative seq encodes causal precedence. With this interpretation, the locative slices are precisely the derivable strings of formulas. Several new technical results about BV are developed as part of this analysis.
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Chapitre d'ouvrage
Categories and Types in Logic, Language, and Physics - Essays Dedicated to Jim Lambek on the Occasion of His 90th Birthday, 8222, Springer, pp.90 - 107, 2014, 〈10.1007/978-3-642-54789-8_6〉
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Richard Blute, Alessio Guglielmi, Ivan T. Ivanov, Prakash Panangaden, Lutz Straßburger. A Logical Basis for Quantum Evolution and Entanglement. Categories and Types in Logic, Language, and Physics - Essays Dedicated to Jim Lambek on the Occasion of His 90th Birthday, 8222, Springer, pp.90 - 107, 2014, 〈10.1007/978-3-642-54789-8_6〉. 〈hal-01092279〉

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