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Reference: Coecke, B and Duncan, R, (2009). Interacting Quantum Observables: Categorical Algebra and Diagrammatics. New Journal of Physics, 13 (4), Article: 043016.Citable link to this page:


Interacting Quantum Observables: Categorical Algebra and Diagrammatics

Abstract: This paper has two tightly intertwined aims: (i) To introduce an intuitiveand universal graphical calculus for multi-qubit systems, the ZX-calculus,which greatly simplifies derivations in the area of quantum computation andinformation. (ii) To axiomatise complementarity of quantum observables within ageneral framework for physical theories in terms of dagger symmetric monoidalcategories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi andsymmetric monoidal categories, our results provide a purely graphicalformalisation of complementarity for quantum observables. Each individualobservable, represented by a commutative special dagger Frobenius algebra,gives rise to an abelian group of phase shifts, which we call the phase group.We also identify a strong form of complementarity, satisfied by the Z and Xspin observables, which yields a scaled variant of a bialgebra.

Peer Review status:Peer reviewedPublication status:PublishedVersion:Publisher's version Funder: Engineering and Physical Sciences Research Council   Funder: Fonds de la Recherche Scientifique   Funder: European Commission   Funder: Foundational Questions Institute   Funder: Office for Nuclear Regulation   Notes:Copyright IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Authors, their institutions and third parties all have the same rights to reuse articles published in New Journal of Physics in accordance with the Creative Commons Attribution 3.0 Unported (CC-BY) license. This allows the articles to be shared, adapted and made commercial use of subject to appropriate attribution.

Bibliographic Details

Publisher: IOP Publishing

Publisher Website:

Journal: New Journal of Physicssee more from them

Publication Website:

Issue Date: 2009-06

pages:Article: 043016Identifiers

Urn: uuid:91391aa8-ac94-4377-8799-e20418b129d1

Source identifier: 303692

Eissn: 1367-2630


Issn: 1367-2630 Item Description

Type: Journal article;

Language: eng

Version: Publisher's versionKeywords: quant-ph quant-ph cs.LO math.CT math.QA Tiny URL: pubs:303692


Author: Coecke, B - institutionUniversity of Oxford Oxford, MPLS, Computer Science - - - Duncan, R - - - - Bibliographic Details Publishe



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