par Coecke, Bob;Duncan, Ross
Référence New journal of physics, 13, 043016
Publication Publié, 2011-04
Article révisé par les pairs
Résumé : 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. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.