Tight bounds for classical and quantum coin flipping

TL;DR

This paper establishes tight bounds for classical and quantum coin flipping protocols, unifying strong and weak variants, and allowing for aborts, thus advancing the understanding of their fundamental limits.

Contribution

It provides a unified framework for strong and weak coin flipping with aborts and derives tight bounds in both classical and quantum settings.

Findings

Tight bounds for classical coin flipping protocols.

Tight bounds for quantum coin flipping protocols.

Unified definition encompassing strong and weak coin flipping.

Abstract

Coin flipping is a cryptographic primitive for which strictly better protocols exist if the players are not only allowed to exchange classical, but also quantum messages. During the past few years, several results have appeared which give a tight bound on the range of implementable unconditionally secure coin flips, both in the classical as well as in the quantum setting and for both weak as well as strong coin flipping. But the picture is still incomplete: in the quantum setting, all results consider only protocols with perfect correctness, and in the classical setting tight bounds for strong coin flipping are still missing. We give a general definition of coin flipping which unifies the notion of strong and weak coin flipping (it contains both of them as special cases) and allows the honest players to abort with a certain probability. We give tight bounds on the achievable range of parameters both in the classical and in the quantum setting.