1999/04/22 by Dominic Mayers, Mayers, Dominic, Louis Salvail +3
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.quant-ph/9904078
openalex publication_date 1999/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In coin tossing two remote participants want to share a uniformly distributed random bit. At the least in the quantum version, each participant test whether or not the other has attempted to create a bias on this bit. It is requested that, for b = 0,1, the probability that Alice gets bit b and pass the test is smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2 holds perfectly against any of the two participants, the task realised is called an exact coin tossing. If the bound is actually 1/2 + ξ where the bias ξ vanishes when a security parameter m defined by the protocol increases, the task realised is a (non exact) coin tossing. It is found here that exact coin tossing is impossible. At the same time, an unconditionally secure quantum protocol that realises a (non exact) coin tossing is proposed. The protocol executes m biased quantum coin tossing procedures at the same time. It executes the first round in each of these m procedures sequentially, then the second rounds are executed, and so on until the end of the n procedures. Each procedure requires 4n particles where n ∈ O(\lg m). The final bit x is the parity of the m random bits. The information about each of these m bits is announced a little bit at a time which implies that the principle used against bit commitment does not apply. The bias on x is smaller than 1/m. The result is discussed in the light of the impossibility result for exact coin tossing.