Quantum coin flipping with arbitrary small bias is impossible

Abstract

Lo and Chau showed that an ideal quantum coin flipping protocol is impossible. The proof was simply derived from the impossibility proof of quantum bit commitment. However, the proof still leaves the possibility of a quantum coin flipping protocol with arbitrary small bias. In this paper, we show that a quantum coin flipping protocol with arbitrary small bias is impossible and show the lower bound of the bias of quantum coin flipping protocol.