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Petri Nets, Discrete Physics, and Distributed Quantum Computation

  • Samson Abramsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5065)

Abstract

We shall describe connections between Petri nets, quantum physics and category theory. The view of Net theory as a kind of discrete physics has been consistently emphasized by Carl-Adam Petri. The connections between Petri nets and monoidal categories were illuminated in pioneering work by Ugo Montanari and José Meseguer. Recent work by the author and Bob Coecke has shown how monoidal categories with certain additional structure (dagger compactness) can be used as the setting for an effective axiomatization of quantum mechanics, with striking applications to quantum information. This additional structure matches the extension of the Montanari-Meseguer approach by Marti-Oliet and Meseguer, motivated by linear logic.

Keywords

Bell State Monoidal Category Linear Logic Monoidal Structure Symmetric Monoidal Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Samson Abramsky
    • 1
  1. 1.Oxford University Computing Laboratory 

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