Coecke, Bob and Duncan, Ross (2011) Interacting quantum observables : categorical algebra and diagrammatics. New Journal of Physics, 13 (April). ISSN 1367-2630Full text not available in this repository. Request a copy from the Strathclyde author
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.
|Keywords:||computational physics, quantum observables, categorical algebra, diagrammatics, Electronic computers. Computer science, Computer Science(all)|
|Subjects:||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:||24 Mar 2017 08:43|