Related papers: Random problems with R
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…
The generation of random numbers via quantum processes is an efficient and reliable method to obtain true indeterministic random numbers that are of vital importance to cryptographic communication and large-scale computer modeling. However,…
We demonstrate a quantum random number generator based on the random nature of the phase difference between two independent laser sources. The speed of random bit generation is determined by the photodetector bandwidth and the linewidth of…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
Semi-quantum cryptography involves at least one user who is semi-quantum or "classical" in nature. Such a user can only interact with the quantum channel in a very restricted way. Many semi-quantum key distribution protocols have been…
In this paper, we present a universal scheme for transforming an arbitrary algorithm for biased 2-face coins to generate random bits from the general source of an m-sided die, hence enabling the application of existing algorithms to general…
We investigate the problem of generating common randomness (CR) from finite compound sources aided by unidirectional communication over rate-limited perfect channels. The two communicating parties, often referred to as terminals, observe…
Non-deterministic random bits are needed in many scientific fields. Unfortunately today's computers are very limited in ability to produce them. We present here a method for extraction of non-deterministic random bits from random physics…
We give an AM protocol that allows the verifier to sample elements x from a probability distribution P, which is held by the prover. If the prover is honest, the verifier outputs (x, P(x)) with probability close to P(x). In case the prover…
We present a random number generation scheme based on measuring the phase fluctuations of a laser with a simple and compact experimental setup. A simple model is established to analyze the randomness and the simulation result based on this…
We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…
This work introduces two new techniques for random number generation with any prescribed nonlinear distribution based on the k-vector methodology. The first approach is based on inverse transform sampling using the optimal k-vector to…
Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…
Random number generators (RNG) based on quantum mechanics are captivating due to their security and unpredictability compared to conventional generators, such as pseudo-random number generators and hardware-random number generators. This…
Recent advances in predictive data analytics and ever growing digitalization and connectivity with explosive expansions in industrial and consumer Internet-of-Things (IoT) has raised significant concerns about security of people's…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…
The standard randomized benchmarking protocol requires access to often complex operations that are not always directly accessible. Compiler optimization does not always ensure equal sequence length of the directly accessible universal gates…
Standard training techniques for neural networks involve multiple sources of randomness, e.g., initialization, mini-batch ordering and in some cases data augmentation. Given that neural networks are heavily over-parameterized in practice,…
This paper studies the counting problem in random dynamical systems. We noticed that the nature of counting in the random setting is completely different than that of the deterministic systems in the sense that non-exponential growth is…