Gap between classical and quantum communication complexities
(S. Y. Zhang)

Communication complexity characterizes the minimal amount of communication needed to compute a function with distributive inputs, and it has numerous connections and applications to other theoretical areas. How much communication can be saved by sending quantum messages? Though this is probably the most fundamental question about quantum communication complexity, our understandings of it are embarrassingly limited. The aim of this project is to attack this notorious open problem itself, as well as to study why our progress has been very little so far.