Quantum weak coin-flipping with bias of 0.192

TL;DR

This paper introduces a family of quantum weak coin-flipping protocols that asymptotically reach a bias of 0.192, improving previous bounds using semidefinite programming analysis.

Contribution

It presents new quantum coin-flipping protocols with lower bias and provides an analytical dual solution to bound cheating probabilities.

Findings

Protocols with n+2 messages achieve biases close to 0.192

n=2 protocol matches Spekkens-Rudolph bias of 0.207

n=8 protocol achieves bias of 0.193

Abstract

A family of protocols for quantum weak coin-flipping which asymptotically achieve a bias of 0.192 is described in this paper. The family contains protocols with n+2 messages for all n>1. The case n=2 is equivalent to the protocol of Spekkens and Rudolph with bias of 0.207. The case n=3 achieves a bias of 0.199, and n=8 achieves a bias of 0.193. The analysis of the protocols uses Kitaev's description of coin-flipping as a semidefinite program. The paper constructs an analytical solution to the dual problem which provides an upper bound on the amount that a party can cheat.