Symmetry principles and quantum resource theories
Symmetry is central to physics, particularly in areas such as particle physics. My project aims to bring symmetry principles more explicitly into quantum information theory. Inspired by the study of entanglement, a resource theory of asymmetry has been formulated. This views asymmetry as a valuable resource that can be used to perform novel information-theoretic tasks. The resource theory perspective of asymmetry has application in the study of thermodynamics in the quantum world. Measurement needs asymmetry, so applying the theory in metrology may allow for more precise measurements.
Symmetry is a geometric property; it is therefore logical to use the mathematical tools of geometry to study symmetry properties. My project has begun to look at the shapes associated with quantum states as a way to measure and classify their asymmetry. This gives a topological classification of the states – the aim is to add finer geometric measures of asymmetry on top of this to give a more detailed picture of the symmetry properties in quantum processes. For example, concepts from information geometry (such as the Fisher information) can be applied in metrology.
The project also seeks to apply the lessons learnt from the resource theory of asymmetry to deduce general properties of resource theories, potentially offering further insight into other theories, including entanglement and thermodynamics.