Interacting quantum observables : categorical algebra and diagrammatics
Coecke, Bob and Duncan, Ross (2011) Interacting quantum observables : categorical algebra and diagrammatics. New Journal of Physics, 13 (April). 043016. ISSN 1367-2630 (https://doi.org/10.1088/1367-2630/13/4/043016)
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Abstract
This paper has two tightly intertwined aims: (i) to introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatize complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi and dagger symmetric monoidal categories, our results provide a purely graphical formalisation of complementarity for quantum observables. Each individual observable, 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 X-spin observables, which yields a scaled variant of a bialgebra.
ORCID iDs
Coecke, Bob and Duncan, Ross ORCID: https://orcid.org/0000-0001-6758-1573;-
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Item type: Article ID code: 45317 Dates: DateEventApril 2011PublishedSubjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 22 Oct 2013 15:51 Last modified: 13 Oct 2024 06:43 URI: https://strathprints.strath.ac.uk/id/eprint/45317