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Recently, a physically realistic protocol amplifying the randomness ofSantha-Vazirani sources producing cryptographically secure random bits wasproposed; however for reasons of practical relevance, the crucial questionremained open whether this can be accomplished under the minimal conditionsnecessary for the task. Namely, is it possible to achieve randomnessamplification using only two no-signaling components and in a situation wherethe violation of a Bell inequality only guarantees that some outcomes of thedevice for specific inputs exhibit randomness? Here, we solve this question andpresent a device-independent protocol for randomness amplification ofSantha-Vazirani sources using a device consisting of two non-signalingcomponents. We show that the protocol can amplify any such source that is notfully deterministic into a fully random source while tolerating a constantnoise rate and prove the composable security of the protocol against generalno-signaling adversaries. Our main innovation is the proof that even thepartial randomness certified by the two-party Bell test (a single input-outputpair ($\textbf{u}^*, \textbf{x}^*$) for which the conditional probability$P(\textbf{x}^* | \textbf{u}^*)$ is bounded away from $1$ for all no-signalingstrategies that optimally violate the Bell inequality) can be used foramplification. We introduce the methodology of a partial tomographic procedureon the empirical statistics obtained in the Bell test that ensures that theoutputs constitute a linear min-entropy source of randomness. As a technicalnovelty that may be of independent interest, we prove that the Santha-Vaziranisource satisfies an exponential concentration property given by a recentlydiscovered generalized Chernoff bound.

Randomness amplification against no-signaling adversaries using two devices