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arXiv · 1711.02662

Simple proof of the impossibility of bit-commitment in generalised probabilistic theories using cone programming

Jamie Sikora·John Selby
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Abstract

Bit-commitment is a fundamental cryptographic task, in which Alice commits a bit to Bob such that she cannot later change the value of the bit, while, simultaneously, the bit is hidden from Bob. It is known that ideal bit-commitment is impossible within quantum theory. In this work, we show that it is also impossible in generalised probabilistic theories (under a small set of assumptions) by presenting a quantitative trade-off between Alice's and Bob's cheating probabilities. Our proof relies crucially on a formulation of cheating strategies as cone programs, a natural generalisation of semidefinite programs. In fact, using the generality of this technique, we prove that this result holds for the more general task of integer-commitment.

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Jamie Sikora, John Selby. 2017-11-07. Simple proof of the impossibility of bit-commitment in generalised probabilistic theories using cone programming. https://doi.org/10.1103/physreva.97.042302

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