I am interested in exploring the mathematical foundations of quantum phenomena such as entanglement using high level mathematical tools and in probing how and why such phenomena work and filtering the ideas of quantum physics down to their minimal mathematical representations. I am currently mainly working on unitary error bases, mutually unbiased bases, quantum homomorphisms and quantum combinatorics. My work has applications to areas such as quantum error correction, quantum state tomography and quantum nonlocal games.
Here is the work I have completed to date:
- Jamie Vicary and I wrote a paper in 2015 introducing quantum Latin squares, as a new generalisation of the combinatorial objects Latin squares. We show how an entirely new class of unitary error bases can be constructed using quantum Latin squares.
- My MSc thesis was written on the same subject as the above paper but is written from a categorical perspective, utilising the graphical calculus of categorical quantum mechanics.
- I have a paper using introducing a diagramatic language for finite fields (here).
- I have written two papers, the latter with Jamie Vicary concerning orthogonality of quantum Latin squares with constructions for mutually unbiased bases and quantum error codes (here and here).
- Recently with fellow DPhil students Dominic Verdon and David Reutter I have written two papers on quantum morphisms and quantum sets combining nonlocal games noncommutative topology with higher categorical techniques (here and here).
I was an Undergratuate in Mathematics at the University of Manchester, before living and working in Asia for several years and studying law. I am now pursuing a doctoral degree in the Quantum Group having completed the MSc in Mathematics and the Foundations of Computer Science in 2014 also at the University of Oxford.