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arXiv · 1610.05140

Certified randomness between mistrustful players

Carl A. Miller·Yaoyun Shi
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Abstract

It is known that if two players achieve a superclassical score at a nonlocal game $G$, then their outputs are certifiably random - that is, regardless of the strategy used by the players, a third party will not be able to perfectly predict their outputs (even if he were given their inputs). We prove that for any complete-support game $G$, there is an explicit nonzero function $F_G$ such that if Alice and Bob achieve a superclassical score of $s$ at $G$, then Bob has a probability of at most $1 - F_G ( s )$ of correctly guessing Alice's output after the game is played. Our result implies that certifying global randomness through such games must necessarily introduce local randomness.

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Carl A. Miller, Yaoyun Shi. 2016-10-17. Certified randomness between mistrustful players. https://arxiv.org/abs/1610.05140

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