We investigate coin-flipping protocols for multiple parties in a quantum broadcast setting:
We propose and motivate a definition for quantum broadcast. Our model of quantum broadcast channel is new. We discovered that quantum broadcast is essentially a combination of pairwise quantum channels and a classical broadcast channel. This is a somewhat surprising conclusion, but helps us in both our lower and upper bounds. We provide tight upper and lower bounds on the optimal bias \varepsilon of a coin which can be flipped by k parties of which exactly g parties are honest: for any 1 \le g \le k,\varepsilon = \frac{1}{2} - \Theta (\frac{g}{k}). Thus, as long as a constant fraction of the players are honest, they can prevent the coin from being fixed with at least a constant probability. This result stands in sharp contrast with the classical setting, where no non-trivial coin-flipping is possible when g \le \frac{k}{2}.
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