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Mochon's proof [Moc07] of existence of quantum weak coin flipping witharbitrarily small bias is a fundamental result in quantum cryptography, but atthe same time one of the least understood. Though used several times as a blackbox in important follow-up results [Gan09, CK09, AS10, CK11, KZ13] the resulthas not been peer-reviewed, its novel techniques (and in particular Kitaev'spoint game formalism) have not been applied anywhere else, and an explicitprotocol is missing. We believe that truly understanding the existence proofand the novel techniques it relies on would constitute a major step in quantuminformation theory, leading to deeper understanding of entanglement and ofquantum protocols in general. In this work, we make a first step in thisdirection. We simplify parts of Mochon's construction considerably, makingabout 20 pages of analysis in the original proof superfluous, clarifying someother parts of the proof on the way, and presenting the proof in a way which isconceptually easier to grasp. We believe the resulting proof of existence iseasier to understand, more readable, and certainly verifiable. Moreover, weanalyze the resources needed to achieve a bias $\epsilon$ and show that thenumber of qubits is $O(\log 1/\epsilon)$, while the number of rounds is$(1/\epsilon)^{O(1/\epsilon)}$. A true understanding of the proof, includingKitaev's point game techniques and their applicability, as well as completingthe task of constructing an explicit (and also simpler and more efficient)protocol, are left to future work.

A simpler proof of existence of quantum weak coin flipping with arbitrarily small bias