I am working with Jamie Vicary and Samson Abramsky on structural aspects of Quantum mechanics and Quantum computation.
During the beginning of my PhD I have been exploring two different areas. The first is category theory; more specifically higher categorical models for quantum mechanics. Together with Jamie Vicary and with Chris Heunen, I have been looking at symmetric monoidal 2-categories which provides a graphical language for quantum protocols, see http://arxiv.org/abs/1405.1463. This is still work in progress.
I am also interested in the mathematical structure of contextuality and the role that it plays in quantum algorithms. The questions that I am exploring are the following: What is the relation between different formalisations of contextuality? How can contextuality be defined abstractly in full generality? What is the role of contextuality in quantum computing? Can it be a resource for quantum algorithms to provide a speedup over classical algorithms?
I studied mathematics at the Vrije Universiteit in Amsterdam, focussing on topology, algebra, probability theory and logic. After that I did the MSc. Mathematics and the Foundations of of Computer Science at the University of Oxford, looking at category theory, quantum computing and algebraic topology. My MSc. thesis was on categorical models for quantum mechanics: http://www.cs.ox.ac.uk/people/bob.coecke/Linde_thesis.pdf