In no particular order:

* the relationships between fundamental principles of quantum theory and other physical theories
and information theoretic tasks. An example is the first secure key distribution scheme based on the no-signalling principle, which Jonathan Barrett, Lucien Hardy and I devised.
* the quantum reality problem, and specifically finding theories that respect special relativity and quantum theory and that also supply an explicitly realist ontology.
* the physics of decoherence and its implications for fundamental physics
* novel tests of quantum theory and alternative theories
* new cryptographic applications of quantum information
* new scientific applications of quantum information.

I am currently co-editing and contributing to a book, "Many Worlds? Everett, Quantum Theory and Reality", with Simon Saunders, Jonathan Barrett and David Wallace, to be published by Oxford University Press. My chapter reviews recent ideas in the Everettian literature from a critical perspective. I argue in particular that we can (despite the claims of my Everettians) find a satisfactory account of the scientific treatment of one-world theories involving apparently random data, and that there is no satisfactory parallel treatment of many-worlds theories. I also point out some (I think insuperable) problems with recent attempts to describe how many-worlds theories can be confirmed or disconfirmed by evidence. And I explain why the attempt to reinterpret the Born weights as some form of "caring measure" in Everettian quantum theory aren't rationally compelling. A version of the chapter will appear on the quant-ph arxiv in due course.

More details of past, present and future research may appear on my personal website from time to time.