A New Protocol and Lower Bounds for Quantum Coin Flipping

Details A New Protocol and Lower Bounds for Quantum Coin Flipping A New Protocol and Lower Bounds for Quantum Coin Flipping

2002-04-04

arxiv.org/abs/quant-ph/0204022v1

Journal of Computer and System Sciences, 68(2): 398-416, 2004.

Physics

Quantum Physics

20 pages, submitted to Journal of Computer and System Sciences, earlier version in proceedings of STOC'01

Scientific paper

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.)

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