Picture of person typing on laptop with programming code visible on the laptop screen

World class computing and information science research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by researchers from the Department of Computer & Information Sciences involved in mathematically structured programming, similarity and metric search, computer security, software systems, combinatronics and digital health.

The Department also includes the iSchool Research Group, which performs leading research into socio-technical phenomena and topics such as information retrieval and information seeking behaviour.

Explore

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). ISSN 1367-2630

[img]
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.