My work is focused on categorical and algebraic structures and their applications in quantum information. Some key interests are: topological quantum field theory, quantum information, categorical quantum mechanics, tensor categories, bicategories, etc. Some recent research is indicated below.
- With Jamie Vicary I am investigating quantum protocols in the situation of reference frame misalignment (or equivalently, charge conservation):
- 'Perfect tight quantum teleportation without a shared reference frame.' (https://arxiv.org/abs/1710.01060). Shows that for finite reference frames perfect teleportation may often be achieved with no communication of reference frame information. (A very early version of this work appeared in the proceedings of QPL 2016 as 'Tight reference frame independent quantum teleportation'.)
- A paper on application of this approach to infinite reference frames is in preparation.
- In 'Coherence for braided and symmetric pseudomonoids' (I extend the coherence theorems for braided and symmetric monoidal categories to arbitrary braided and symmetric pseudomonoids using diagrammatic 'movie' calculus. This work is a categorification of the theory of PROs, PROBs and PROPs for monoids and commutative monoids. I recently gave two talks about this work at HDRA2017 and PSSL 101; the slides are available here.