Quantum dice rolling: a multi-outcome generalization of quantum coin flipping

Abstract

We generalize the problem of coin flipping to more than two outcomes and\nparties. We term this problem dice rolling, and study both its weak and strong\nvariants. We prove by construction that in quantum settings (i) weak N-sided\ndice rolling admits an arbitrarily small bias for any value of N, and (ii)\ntwo-party strong N-sided dice rolling saturates the corresponding\ngeneralization of Kitaev's bound for any value of N. In addition, we make use\nof this last result to introduce a family of optimal 2m-party strong n^m-sided\ndice rolling protocols for any value of m and n.\n