Compositional Quantum Logic

Bob Coecke, Chris Heunen, Aleks Kissinger

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

Abstract / Description of output

Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles’ heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We introduce a framework in which order-theoretic structure comes with a primitive composition operation. The order is extracted from a generalisation of C*-algebra that applies to arbitrary dagger symmetric monoidal categories, which also provide the composition operation. In fact, our construction is entirely compositional, without any additional assumptions on limits or enrichment. Interpreted in the category of finite-dimensional Hilbert spaces, it yields the projection lattices of arbitrary finite-dimensional C*-algebras. Interestingly, there are models that falsify standardly assumed correspondences, most notably the correspondence between noncommutativity of the algebra and nondistributivity of the order.
Original languageEnglish
Title of host publicationComputation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky
Subtitle of host publicationEssays Dedicated to Samson Abramsky on the Occasion of His 60th Birthday
EditorsBob Coecke, Luke Ong, Prakash Panangaden
PublisherSpringer Berlin Heidelberg
Number of pages16
ISBN (Electronic)978-3-642-38164-5
ISBN (Print)978-3-642-38163-8
Publication statusPublished - 2013

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin Heidelberg


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