Large family of quantum weak coin-flipping protocols
Carlos Mochon · Physical Review A · 2005
Each classical public-coin protocol for coin flipping is naturally associated with a quantum protocol for weak coin flipping. The quantum protocol is obtained by replacing classical randomness with quantum entanglement and by adding a cheat detection test in the last round that verifies the integrity of this entanglement. The set of such protocols defines a family which contains the protocol with bias 0.192 previously found by the author, as well as protocols with bias as low as $1∕6$ described herein. The family is analyzed by identifying a set of optimal protocols for every number of messages. In the end, tight lower bounds for the bias are obtained which prove that $1∕6$ is optimal for all protocols within the family.