Interacting quantum observables: categorical algebra and diagrammatics

Details Interacting quantum observables: categorical algebra and diagrammatics Interacting quantum observables: categorical algebra and diagrammatics

Apr 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011njph...13d3016c&link_type=abstract

New Journal of Physics, Volume 13, Issue 4, pp. 043016 (2011).

Physics

Scientific paper

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.

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