Quantum versus Randomized Communication Complexity, with Efficient Players

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 partial Boolean function f over inputs length N, such that: Items (1), (2) match proved (2016). Item (3) new. (Our incomparable one Gavinsky. While he quantitatively better lower bound $$\Omega\left(N^{1/2}\right)$$ case, referee his inefficient). Exponential have been studied numerous previous works, but best our knowledge efficiency has not addressed, most seem inefficient. The only know efficient recent based on lifting Göös et al. (2017), Chattopadhyay (2019a). However, these require at least two rounds communication, so imply two-way do stronger simultaneous-message vs. (or even one-way complexity). proof technique completely new, context techniques from Raz & Tal (2019). lift forrelation problem, xor as gadget.