Quantum dice rolling

TL;DR

This paper demonstrates that quantum resources enable N parties to roll an N-sided dice with arbitrarily small bias, and introduces a specific protocol for three-sided dice rolling with a bias of 0.181.

Contribution

It extends quantum coin flipping to N-sided dice rolling with arbitrarily small bias and presents a new six-round protocol for three-sided dice.

Findings

N-sided dice rolling with arbitrarily small bias is possible quantum mechanically.

A six-round protocol for three-sided dice rolling with bias 0.181 is proposed.

Quantum dice rolling surpasses classical limitations.

Abstract

A coin is just a two sided dice. Recently, Mochon proved that quantum weak coin flipping with an arbitrarily small bias is possible. However, the use of quantum resources to allow N remote distrustful parties to roll an N-sided dice has yet to be addressed. In this paper we show that contrary to the classical case, N-sided dice rolling with arbitrarily small bias is possible for any N. In addition, we present a six-round three-sided dice rolling protocol, achieving a bias of 0.181, which incorporates weak imbalanced coin flipping.