We are running a seminar among PhDs in math and try to learn some quantum information theory and quantum computation. Being an analyst I'd like to make a contribution with a topic in that direction. I faintly remember listening to a talk about "quantum information and non-local games" where they discussed a more analytic approach to those things (mentioning also how things become more complicated when the Hilbert spaces are no longer finite-dimensional). In case somebody has a nice introductory reference I'd love to hear it. Also if you have a topic similar in spirit, I'd be happy to learn about it.
Until now we covered big chunks of “Classical and Quantum Computation” (di Alexei Yu. Kitaev, Alexander Shen, Mikhail N. Vyalyi, M. N. Vyalyi). The background of the attending PhDs is diverse (ranging from crypto people over combinators to mathematical physics).