Le contenu de cette page n’est pas disponible en français. Veuillez nous en excuser.
 

Explicit quantum weak coin flipping protocols with arbitrarily small bias



Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other compatible player.


Recording Details

Speaker(s): 
Scientific Areas: 
PIRSA Number: 
20030088

Abstract

We investigate weak coin flipping, a fundamental cryptographic primitive where two distrustful parties need to remotely establish a shared random bit. A cheating player can try to bias the output bit towards a preferred value. A weak coin-flipping protocol has a bias ϵ if neither player can force the outcome towards their preferred value with probability more than 1/2+ϵ. While it is known that classically ϵ=1/2, Mochon showed in 2007 [arXiv:0711.4114] that quantumly weak coin flipping can be achieved with arbitrarily small bias, i.e. ϵ(k)=1/(4k+2) for arbitrarily large k, and he proposed an explicit protocol approaching bias 1/6. So far, the best known explicit protocol is the one by Arora, Roland and Weis, with ϵ(2)=1/10 (corresponding to k=2) [STOC'19, p. 205-216]. In the current work, we present the construction of protocols approaching arbitrarily close to zero bias, i.e. ϵ(k) for arbitrarily large k. We connect the algebraic properties of Mochon's assignments---at the heart of his proof of existence---with the geometric properties of the unitaries whose existence he proved. It is this connection that allows us to find these unitaries analytically.