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

[thumbnail of Coecke-Duncan-NJP-2011-Interacting-quantum-observables-categorical-algebra-and-diagrammatics]
Preview
 Text (Coecke-Duncan-NJP-2011-Interacting-quantum-observables-categorical-algebra-and-diagrammatics)
Coecke_Duncan_NJP_2011_Interacting_quantum_observables_categorical_algebra_and_diagrammatics.pdf
Final Published Version
License: Creative Commons Attribution-NonCommercial-ShareAlike 3.0 logo
Download (2MB)| Preview

    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 logoORCID: https://orcid.org/0000-0001-6758-1573;
    CORE (COnnecting REpositories)