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Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
In 1909 Borel defined normality as a notion of randomness of the digits of the representation of a real number over certain base (fractional expansion). If we think the representation of a number over a base as an infinite sequence of…
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any…
Macroscopic quantum phenomena, such as observed in superfluids and superconductors, have led to promising technological advancements and some of the most important tests of fundamental physics. At present, quantum detection of light is…
The generation of series of random numbers is an important and difficult problem. Even the very definition of random is difficult. Appropriate measurements on entangled states have been proposed as the definitive solution to produce series…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
The generation of random bits is of enormous importance in modern information science. Cryptographic security is based on random numbers which require a physical process for their generation. This is commonly performed by hardware random…
Quantum Random Number Generators (QRNGs) emerged as a promising solution for generating truly random numbers. In the present article, we give an overview of QRNGs highlighting the merits and demerits of various strategies briefly. Then…
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…
We present an efficient method to extract the amount of true randomness that can be obtained by a Quantum Random Number Generator (QRNG). By repeating the measurements of a quantum system and by swapping between two mutually unbiased bases,…
The certification of randomness is essential for both fundamental science and information technologies. Unlike traditional random number generators, randomness obtained from nonlocal correlations is fundamentally guaranteed to be…
How to generate genuine quantum randomness from untrusted devices is an important problem in quantum information processing. Inspired by previous work on a self-testing quantum random number generator [T. Lunghi et al., Phys. Rev. Lett.…
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true…
We present experimental results on the effects of using quantum or 'truly' random numbers, as opposed to pseudorandom numbers, in a system that exhibits computational creativity (given its ability to compose original chess problems). The…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
The unpredictability of random numbers is fundamental to both digital security and applications that fairly distribute resources. However, existing random number generators have limitations-the generation processes cannot be fully traced,…
Random features are a powerful technique for rewriting positive-definite kernels as linear products. They bring linear tools to bear in important nonlinear domains like KNNs and attention. Unfortunately, practical implementations require…
We present a randomized polynomial-time algorithm to generate a random integer according to the distribution of norms of ideals at most N in any given number field, along with the factorization of the integer. Using this algorithm, we can…
Random numbers are used in a wide range of sciences. In many applications, generating unpredictable private random numbers is indispensable. Device-independent quantum random number generation is a framework that makes use of the intrinsic…
Ideal quantum random number generators (QRNGs) can produce algorithmically random and thus incomputable sequences, in contrast to pseudo-random number generators. However, the verification of the presence of algorithmic randomness and…