A new protocol and lower bounds for quantum coin flipping

Andris Ambainis

Abstract: 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 ε, it must use at least Ω(loglog1ε)<math><mtext>Ω(</mtext><mtext>log</mtext><mspace xmlns="true" sp="0.16" width="2px" linebreak="nobreak" is="true"></mspace><mtext>log</mtext><mspace xmlns="true" sp="0.16" width="2px" linebreak="nobreak" is="true"></mspace><mtext>1</mtext><mtext>ε</mtext><mtext>)</mtext></math> 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.)