We give the first exponential separation between quantum and
classical multi-party
communication complexity in the (non-interactive) one-way and
simultaneous message
passing settings.
For every k, we demonstrate a relational communication problem
between k parties
that can be solved exactly by a quantum simultaneous message passing
protocol of
cost ... more >>>

We improve the best known upper bounds on the density of corner-free sets over quasirandom groups from inverse poly-logarithmic to quasi-polynomial. We make similarly substantial improvements to the best known lower bounds on the communication complexity of a large class of permutation functions in the 3-player Number-on-Forehead model. Underpinning both ... more >>>