A Logical Basis for Quantum Evolution and Entanglement

  • Richard F. Blute
  • Alessio Guglielmi
  • Ivan T. Ivanov
  • Prakash Panangaden
  • Lutz Straßburger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8222)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Richard F. Blute
    • 1
  • Alessio Guglielmi
    • 2
  • Ivan T. Ivanov
    • 3
  • Prakash Panangaden
    • 4
  • Lutz Straßburger
    • 5
  1. 1.Department of Mathematics and StatisticsUniversity of OttawaCanada
  2. 2.Department of Computer ScienceUniversity of BathUK
  3. 3.Department of MathematicsVanier CollegeCanada
  4. 4.School of Computer ScienceMcGill UniversityCanada
  5. 5.INRIA Saclay, École PolytechniqueFrance

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