Randomness Amplification under Minimal Fundamental Assumptions on the Devices.

Recently, the physically realistic protocol amplifying the randomness of Santha-Vazirani sources producing cryptographically secure random bits was proposed; however, for reasons of practical relevance, the crucial question remained open regarding whether this can be accomplished under the minimal conditions necessary for the task. Namely, is it possible to achieve randomness amplification using only two no-signaling 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 device-independent protocol for randomness amplification of Santha-Vazirani 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 no-signaling adversaries. Our main innovation is the proof that even the partial randomness certified by the two-party Bell test [a single input-output pair (u^{*}, x^{*}) for which the conditional probability P(x^{*}|u^{*}) is bounded away from 1 for all no-signaling 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 min-entropy source of randomness. As a technical novelty that may be of independent interest, we prove that the Santha-Vazirani source satisfies an exponential concentration property given by a recently discovered generalized Chernoff bound.

Realistic noise-tolerant randomness amplification using finite number of devices.

Randomness is a fundamental concept, with implications from security of modern data systems, to fundamental laws of nature and even the philosophy of science. Randomness is called certified if it describes events that cannot be pre-determined by an external adversary. It is known that weak certified randomness can be amplified to nearly ideal randomness using quantum-mechanical systems. However, so far, it was unclear whether randomness amplification is a realistic task, as the existing proposals either do not tolerate noise or require an unbounded number of different devices. Here we provide an error-tolerant protocol using a finite number of devices for amplifying arbitrary weak randomness into nearly perfect random bits, which are secure against a no-signalling adversary. The correctness of the protocol is assessed by violating a Bell inequality, with the degree of violation determining the noise tolerance threshold. An experimental realization of the protocol is within reach of current technology.