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# Quantum weak coin flipping with a single photon

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### Abstract

Weak coin flipping is among the fundamental cryptographic primitives which ensure the security of modern communication networks. It allows two mistrustful parties to remotely agree on a random bit when they favor opposite outcomes. Unlike other two-party computations, one can achieve information-theoretic security using quantum mechanics only: both parties are prevented from biasing the flip with probability higher than $$1/2+\epsilon$$, where $$\epsilon$$ is arbitrarily low. Classically, the dishonest party can always cheat with probability $$1$$ unless computational assumptions are used. Despite its importance, no physical implementation has been proposed for quantum weak coin flipping. Here, we present a practical protocol that requires a single photon and linear optics only. We show that it is fair and balanced even when threshold single-photon detectors are used, and reaches a bias as low as $$\epsilon=1/\sqrt{2}-1/2\approx 0.207$$. We further show that the protocol may display quantum advantage over a few hundred meters with state-of-the-art technology.

### Author and article information

###### Journal
20 February 2020
###### Article
2002.09005