Operational theories and Categorical quantum mechanics

Samson Abramsky, Chris Heunen

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative theories. Two formalisms which have been used in this context are operational theories, and categorical quantum mechanics. The aim of the present paper is to establish strong connections between these two formalisms. We show how models of categorical quantum mechanics have representations as operational theories. We then show how nonlocality can be formulated at this level of generality, and study a number of examples from this point of view, including Hilbert spaces, sets and relations, and stochastic maps. The local, quantum, and no-signalling models are characterized in these terms.
Original languageEnglish
Title of host publicationLogic and Algebraic Structures in Quantum Computing
PublisherCambridge University Press
Number of pages37
ISBN (Print)9781107033399
Publication statusPublished - Mar 2016

Publication series

NameLecture Notes in Logic
Volume45

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