摘要：We present two parallel repetition theorems for the entangled value of multi-player, one-round free games (games where the inputs come from a product distribution). Our first theorem shows that for a k-player free game G with entangled value val^*(G) = 1 - epsilon, the n-fold repetition of G has entangled value val^*(G^(\otimes n)) at most (1 - epsilon^(3/2))^(Omega(n/sk^4)), where s is the answer length of any player. In contrast, the best known parallel repetition theorem for the classical value of two-player free games is val(G^(\otimes n)) = 1 such that val^*(G^(\otimes n)) >= val^*(G)^(n/k). Our analysis exploits the novel connection between communication protocols and quantum parallel repetition, first explored by Chailloux and Scarpa (ICALP 2014). We demonstrate that better communication protocols yield better parallel repetition theorems: in particular, our first theorem crucially uses a quantum search protocol by Aaronson and Ambainis, which gives a quadratic Grover speed-up for distributed search problems. Finally, our results apply to a broader class of games than were previously considered before; in particular, we obtain the first parallel repetition theorem for entangled games involving more than two players, and for games involving quantum outputs.
关键词：Parallel repetition; quantum entanglement; communication complexity
