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.
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 language  English 

Title of host publication  Categories and Types in Logic, Language, and Physics 
Editors  C. Casadio, B. Coecke, M. Moortgat, P. Scott 
Publisher  Springer 
Pages  90107 
Number of pages  18 
Volume  8222 
ISBN (Electronic)  9783642547898 
ISBN (Print)  9783642547881 
DOIs  
Publication status  Published  31 Dec 2014 
Publication series
Name  Lecture Notes in Computer Science 

Publisher  Springer 
Volume  8222 
Fingerprint
Dive into the research topics of 'A logical basis for quantum evolution and entanglement'. Together they form a unique fingerprint.Profiles

Alessio Guglielmi
Person: Research & Teaching