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arXiv · 1901.04876

On the impossibility of coin-flipping in generalized probabilistic theories via discretizations of semi-infinite programs

Jamie Sikora·John H. Selby
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Abstract

Coin-flipping is a fundamental cryptographic task where a spatially separated Alice and Bob wish to generate a fair coin-flip over a communication channel. It is known that ideal coin-flipping is impossible in both classical and quantum theory. In this work, we give a short proof that it is also impossible in generalized probabilistic theories under the Generalized No-Restriction Hypothesis. Our proof relies crucially on a formulation of cheating strategies as semi-infinite programs, i.e., cone programs with infinitely many constraints. This introduces a new formalism which may be of independent interest to the quantum community.

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Jamie Sikora, John H. Selby. 2019-01-15. On the impossibility of coin-flipping in generalized probabilistic theories via discretizations of semi-infinite programs. https://doi.org/10.1103/physrevresearch.2.043128

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