The impossibility of efficient quantum weak coin flipping

Abstract

How can two parties with competing interests carry out a fair coin flip across a quantum communication channel? This problem (quantum weak coin-flipping) was formalized more than 15 years ago, and, despite some phenomenal theoretical progress, practical quantum coin-flipping protocols with vanishing bias have proved hard to find. In the current work we show that there is a reason that practical weak quantum coin-flipping is difficult: any quantum weak coin-flipping protocol with bias " must use at least exp( ω (1/g" )) rounds of communication. This is a large improvement over the previous best known lower bound of ω ( log log(1/" )) due to Ambainis from 2004. Our proof is based on a theoretical construction (the two-variable profile function) which may find further applications.