I am interested in exploring the mathematical foundations of quantum phenomena such as entanglement using high level mathematical tools. I am interested 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, linear algebraic objects fundamental to teleportation, dense coding and quantum error correction. I am also interested in tensor networks and attended the 2015 'Tensor Network Summer School' in Ghent.
Here is the work I have completed to date:
- Jamie Vicary and I have recently written a paper 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. Amongst other things this introduces a new class of teleportation protocols.
- 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 hope to have a new paper soon exploring orthogonality of Latin squares.
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.