Quantum information is the study of how the rules of quantum mechanics affect information processing tasks. In our group, we are interested in the mathematics of quantum information, and in particular, in quantum (or noncommutative) probability, which is the basic mathematical toolkit used in quantum information. Also of special interest is the theory of entanglement, and how this can be used as a resource in many areas, including in nonlocal games, quantum communication, and algorithm design for quantum computers.