My work is focused on categorical and algebraic structures and their applications in quantum information. Some key words are: topological quantum field theory, quantum information, categorical quantum mechanics, tensor categories, bicategories, etc. Some particular areas of research are indicated below.
- I am investigating quantum protocols in the situation of reference frame alignment or charge conservation, from a categorical perspective. Applications include:
- Perfect reference frame independent quantum teleportation for finite RF transformation group actions using certain algebraic structures. A very early version of this work appeared in the proceedings of QPL 2016 as 'Tight reference frame independent quantum teleportation' (https://arxiv.org/abs/1603.08866). A much newer version with a complete classification of such protocols for a qubit will appear soon. This is joint work with Jamie Vicary.
- Increased purity of quantum teleportation for infinite RF transformation group actions, where perfect teleportation is impossible. This is also joint work with Jamie Vicary.
- Possible rate increase for device-dependent RFI QKD (work in progress).
- 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 a higher diagrammatic rewriting approach. This work is a categorification of the theory of PROs, PROBs and PROPs for monoids and commutative monoids.
- I am also working with quantum latin squares and quantum graph homomorphisms.