  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 our protocol is optimal for a certain type of
quantum protocols.
  For arbitrary quantum protocols, we show that if a protocol achieves a bias
of at most $\epsilon$, it must use at least $\Omega(\log \log
\frac{1}{\epsilon})$ 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.)
