In no particular order:

* the relationships between fundamental principles of quantum theory and other physical theories
and information theoretic tasks. One example is the so-called BHK protocol -- the first secure cryptographic key distribution scheme based on the no-signalling principle -- which Jonathan Barrett, Lucien Hardy and I devised. Another, from 2011, is a solution to a longstanding cryptographic problem -- finding a simple and provably unconditionally secure scheme for bit commitment -- that relies essentially on the properties of quantum information in Minkowski space.
* 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
* other novel scientific applications of quantum information.

I recently co-edited "Many Worlds? Everett, Quantum Theory and Reality" (Oxford University Press, 2010). My chapter in the book critically reviews recent attempts to make sense of many-worlds quantum theory, and in particular to make sense of probability within many-worlds quantum theory -- which we clearly need to do if the theory is to reproduce all the probabilistic predictions of standard quantum theory, but which is also clearly (at best) problematic, since many-worlds quantum theory is deterministic. 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.

For more details of past and present research, see my papers on the physics arxiv.