A large family of quantum weak coin-flipping protocols
(February 2005)Abstract
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.
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