Axiomatizing complementarity in infinite dimensions

Quantum mechanics explains the behavior of particles in sub-atomic levels. A feature of quantum mechanics is that measurable properties of physical systems occur in complementary pairs : one can ‘know’ the value of only one of the paired properties at any point in time. For example, measuring the position observable changes the value of the momentum observable since they are complementary.

Recently, a mathematical framework has been developed in which one can describe many quantum phenomena including complementarity using simple diagrams. The diagrammatic framework is developed using Category Theory which is a branch of modern mathematics. The framework can currently describe only finite-dimensional quantum systems. However, there are important quantum systems which are infinite-dimensional such as quantum computers that compute over continuous variables. Hence, there is a practical need to extend the current diagrammatic framework to include infinite-dimensional systems and to describe quantum phenomena in the extended framework. In this project, we generalize the existing diagrammatic framework to describe infinite dimensions and attempt to formalize complementarity in this new framework. We will also apply the formalization to describe some of the existing infinite-dimensional quantum protocols.

Faculty Supervisor:

Robin Cockett

Student:

Partner:

University of Oxford;University of Edinburgh

Discipline:

Computer science

Sector:

Information and Communications Technology; Technology; Quantum Science

University:

University of Calgary

Program: