Improving device-independent weak coin flipping protocols

Abstract

Weak coin flipping is the cryptographic task where Alice and Bob remotely flip a coin but want opposite outcomes. This work studies this task in the device-independent regime where Alice and Bob neither trust each other, nor their quantum devices. The best protocol was devised over a decade ago by Silman, Chailloux, Aharon, Kerenidis, Pironio, and Massar with bias $\varepsilon \approx 0.33664$, where the bias is a commonly adopted security measure for coin flipping protocols. This work presents two techniques to lower the bias of such protocols, namely self-testing and abort-phobic compositions. We apply these techniques to the SCAKPM '11 protocol above and, assuming a continuity conjecture, lower the bias to $\varepsilon \approx 0.29104$. We believe that these techniques could be useful in the design of device-independent protocols for a variety of other tasks. Independently of weak coin flipping, en route to our results, we show how one can test $n-1$ out of $n$ devices, and estimate the performance of the remaining device, for later use in the protocol. The proof uses linear programming and, due to its generality, may find applications elsewhere.