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

TL;DR

This paper extends quantum coin flipping to multi-outcome scenarios, demonstrating that weak N-sided dice rolling can achieve arbitrarily small bias and that strong N-sided dice rolling reaches Kitaev's bound, leading to optimal multi-party protocols.

Contribution

It introduces the concept of dice rolling in quantum settings, proving bias bounds and optimal protocols for multi-outcome, multi-party quantum dice rolling.

Findings

Weak N-sided dice rolling admits arbitrarily small bias.

Two-party strong N-sided dice rolling saturates Kitaev's bound.

Introduces optimal multi-party dice rolling protocols.

Abstract

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