A new protocol and lower bounds for quantum coin flipping

We present a new protocol and two lower bounds for quantum coin flipping. In our protocol, no dishonest party can achieve one outcome with probability more than 0.75. Then we show that out protocol is optimal among 3-round protocols of a certain form. For arbitrary quantum protocols, we show that if a protocol achieves a bias of at most epsilon, it must use at least Omega(log log(1)/(epsilon)) rounds of communication. This implies that the parallel repetition fails for quantum coin flipping. (The bias of a protocol cannot be arbitrarily decreased by running several copies of it in parallel.) (C) 2003 Elsevier Inc. All rights reserved.