Supervisors: 

David Jennings

Irreversibility and symmetry in quantum mechanics

The theory of asymmetry is a very young framework and is underdeveloped compared to the well-established notions of symmetry. It can be used to analyse the far more ubiquitous occurrence of asymmetry in dynamics, but can moreover allow for a model of global symmetry that arises from locally asymmetric dynamics. Our research will focus on applying some of the recent machinery that has been developed in asymmetry theory to quantum thermodynamics and gauge theory type formulations in quantum information.

One of the ways in which we hope to extend quantum thermodynamics is by asking what it means for a system to be truly quantum. Theories of quantum coherence and non-local correlations have been extensively studied in a thermodynamic setting, but the introduction of non-commuting observables to these systems remains to be studied. If we have a system with dynamics that conserve some observable quantities, then we naturally think of these as a symmetry of the system. In the case of a quantum system, these observables can be non-commuting and be represented by a non-Abelian symmetry group. This should give rise to thermodynamic properties that are genuinely non classical! It is reasonable to subsequently ask how these dynamics with non-Abelian symmetries affect the system’s ability to do work.

Further extensions will involve how local quantum resources can flow through a general, causal quantum network and the study of local and global symmetries from an information-theoretic and thermodynamic perspective. Beyond this, the framework may be applied to generalisations of Noether’s theorem for quantum systems.