A logical basis for quantum evolution and entanglement

Richard Blute, A Guglielmi, Ivan Ivanov, Prakash Panangaden, Lutz Straßburger

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

Abstract

We reconsider discrete quantum causal dynamics where quantum systems are viewed as discrete structures, namely directed acyclic graphs. In such a graph, events are considered as vertices and edges depict 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 influences, but large enough to capture nonlocal correlations.

In our logical interpretation, edges are assigned logical formulas in a special 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 noncommutative 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.
Original languageEnglish
Title of host publicationCategories and Types in Logic, Language, and Physics
EditorsC. Casadio, B. Coecke, M. Moortgat, P. Scott
PublisherSpringer
Pages90-107
Number of pages18
Volume8222
ISBN (Electronic)978-3-642-54789-8
ISBN (Print)978-3-642-54788-1
DOIs
Publication statusPublished - 31 Dec 2014

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume8222

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    Blute, R., Guglielmi, A., Ivanov, I., Panangaden, P., & Straßburger, L. (2014). A logical basis for quantum evolution and entanglement. In C. Casadio, B. Coecke, M. Moortgat, & P. Scott (Eds.), Categories and Types in Logic, Language, and Physics (Vol. 8222, pp. 90-107). (Lecture Notes in Computer Science; Vol. 8222). Springer. https://doi.org/10.1007/978-3-642-54789-8_6