We study a new type of separations between quantum and classical communication complexity, that are obtained using protocols where all parties efficient, in the sense they can be implemented by small circuits, with oracle access to their inputs. Our main result qualitatively matches strongest known separation complexity Gavinsky (2016) is protocol efficient. More precisely, we give an explicit ...

We study the two-party communication complexity of functions with large outputs, and show that can greatly vary depending on what output model is considered. a variety models, ranging from open model, in which an external observer compute outcome, to XOR outcome protocol should be bitwise players’ local outputs. This inspired by games, are widely studied two-player quantum games. focus question...

42 and transmits the index of the set that contains x. By the model assumption he doesn't need to transmit which partition was picked. P Y then, transmits 1 if y belongs to the same set in the partition and 0 otherwise. The number of bits transmitted is 1 + dlog n b1+2(n?1)c e. The error probability is clearly 0 if x = y and, by symmetry or a more cumbersome argument, at most 2 for x 6 = y. As ...