Randomness amplification against nosignaling adversaries using two devices
Abstract
Recently, a physically realistic protocol amplifying the randomness of SanthaVazirani sources producing cryptographically secure random bits was proposed; however for reasons of practical relevance, the crucial question remained open whether this can be accomplished under the minimal conditions necessary for the task. Namely, is it possible to achieve randomness amplification using only two nosignaling components and in a situation where the violation of a Bell inequality only guarantees that some outcomes of the device for specific inputs exhibit randomness? Here, we solve this question and present a deviceindependent protocol for randomness amplification of SanthaVazirani sources using a device consisting of two nonsignaling components. We show that the protocol can amplify any such source that is not fully deterministic into a fully random source while tolerating a constant noise rate and prove the composable security of the protocol against general nosignaling adversaries. Our main innovation is the proof that even the partial randomness certified by the twoparty Bell test (a single inputoutput pair ($\textbf{u}^*, \textbf{x}^*$) for which the conditional probability $P(\textbf{x}^*  \textbf{u}^*)$ is bounded away from $1$ for all nosignaling strategies that optimally violate the Bell inequality) can be used for amplification. We introduce the methodology of a partial tomographic procedure on the empirical statistics obtained in the Bell test that ensures that the outputs constitute a linear minentropy source of randomness. As a technical novelty that may be of independent interest, we prove that the SanthaVazirani source satisfies an exponential concentration property given by a recently discovered generalized Chernoff bound.
 Publication:

arXiv eprints
 Pub Date:
 April 2015
 arXiv:
 arXiv:1504.06313
 Bibcode:
 2015arXiv150406313R
 Keywords:

 Quantum Physics
 EPrint:
 15 pages, 3 figures