True randomness from realistic quantum devices

Abstract

Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is usable for applications, e.g., in cryptography or gambling, where unpredictability is important. To enable such applications a stronger notion of randomness, termed "true randomness", is required, which includes independence from prior information.Quantum systems are particularly suitable for true randomness generation, as their unpredictability can be proved based on physical principles. Practical implementations of Quantum RNGs (QRNGs) are however always subject to noise, i.e., influences which are not fully controlled. This reduces the quality of the raw randomness generated by the device, making it necessary to post-process it. Here we provide a framework to analyse realistic QRNGs and to determine the post-processing that is necessary to turn their raw output into true randomness.

Maximization of Extractable Randomness in a Quantum Random-Number Generator

“…Our framework can also be generalized to encapsulate potential quantum side information by considering the analysis described in Ref. [27]. A detailed cryptoanalysis of our framework can also increase the final throughput of the QRNG [47].…”

“…They constitute a strong extractor which implies that the seed can be reused without sacrificing too much randomness. In recent development of QRNGs [20,22,26,27,43], they have been used to construct hashing functions such as the Toeplitz-hashing matrix. These constructions require a long (but reusable) seed [44].…”

“…We quantify the amount of quantum randomness to the amount of classical noise using a quantum-to-classical-noise ratio (QCNR). When QCNR is low, both the quality and the security of the random sequence generated may be compromised [24,26,27].…”

Source Independent Quantum Walk Random Number Generation

“…Postprocessing: Finally, Alice applies privacy amplification to r, producing a final random string of size . As proven in [26], the hash function used for privacy amplification need only be chosen randomly once and then reused for each run of the protocol for a QRNG protocol of this nature.…”

Certified Quantum Random Numbers from Untrusted Light

“…Consequently, the first step for analysing our experiment is to carefully calibrate and model the realistic photodiodes, which output noisy voltage measurements rather than exact photon numbers. More formally, following the approach of [35], we model the POVM describing our noisy, characterised measurements as a projective measurement on a larger system. For the case of our detectors (see Fig.…”