IQIM Postdoctoral and Graduate Student Seminar

Friday May 28, 2021 11:00 AM

Quantum Weak Coin Flipping—where weakness is a virtue

Speaker: Atul Singh Arora
Location: Online Event

Abstract: In this talk, I will discuss weak coin flipping, a fundamental cryptographic primitive where two distrustful parties need to remotely establish a shared random bit. A cheating party can try to bias the output bit towards a preferred value. For weak coin flipping the parties have known opposite preferred values. By a weak coin flipping protocol with bias ϵ we mean that 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 (the worst possible), Mochon showed in 2007 that quantumly, weak coin flipping can be performed with arbitrarily small bias (near perfect). His non-constructive proof used the so-called point game formalism—a series of equivalent reductions which were introduced by Kitaev to study coin-flipping. He constructed point games with bias ϵ_M(k)=1/(4k+2) to prove the existence. The best known explicit protocol, however, had bias approaching ϵ_M(1)=1/6 (also due to Mochon, 2005).

In our work, we try to make the non-constructive part of the proof constructive, to wit, we make three main contributions towards the conversion of point-games into explicit protocols. First, we propose a framework—TIPG-to-Explicit-protocol Framework (TEF)—which simplifies the task of constructing explicit protocols. We use this framework to construct a protocol with bias ϵ_M(2)=1/10. We then give the exact formulae for the unitaries corresponding to the point-games due to Mochon, allowing us to describe (almost) perfect coin flipping protocols analytically, i.e. with bias ϵ_M(k) for arbitrarily large k. Finally, we introduce an algorithm we call the Elliptic Monotone Align (EMA) algorithm. This algorithm, together with TEF, lets us convert any point-game into an explicit protocol numerically. We conclude by giving another analytic construction of unitaries for Mochon's games using the ellipsoid picture introduced for the EMA algorithm.

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Series IQIM Postdoctoral and Graduate Student Seminar Series

Contact: Marcia Brown at 626-395-4013