Related papers: An efficient construction of Raz's two-source rand…
In successive refinement of information, the decoder refines its representation of the source progressively as it receives more encoded bits. The rate-distortion region of successive refinement describes the minimum rates required to attain…
Capacities on a finite set are sets functions vanishing on the empty set and being monotonic w.r.t. inclusion. Since the set of capacities is an order polytope, the problem of randomly generating capacities amounts to generating all linear…
We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…
A common disadvantage in existing distribution-free two-sample testing approaches is that the computational complexity could be high. Specifically, if the sample size is $N$, the computational complexity of those two-sample tests is at…
Dodis and Wichs introduced the notion of a non-malleable extractor to study the problem of privacy amplification with an active adversary. A non-malleable extractor is a much stronger version of a strong extractor. Previously, there are…
We prove that random low-degree polynomials (over $\mathbb{F}_2$) are unbiased, in an extremely general sense. That is, we show that random low-degree polynomials are good randomness extractors for a wide class of distributions. Prior to…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
We (claim to) prove the extremely surprising fact that NP=RP. It is achieved by creating a Fully Polynomial-Time Randomized Approximation Scheme (FPRAS) for approximately counting the number of independent sets in bounded degree graphs,…
Seeded extractors are fundamental objects in pseudorandomness and cryptography, and a deep line of work has designed polynomial-time seeded extractors with nearly-optimal parameters. However, existing constructions of seeded extractors with…
Random party distillation refers to the process by which Einstein-Podolsky-Rosen pairs are randomly extracted from a single copy of a multipartite entangled state after multiple rounds of performing positive operator value measure…
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts---a randomness source and its readout. The source is…
Random number generation (RNG) is a crucial element in security protocols, and its performance and reliability are critical for the safety and integrity of digital systems. This is especially true in 5G networks with many devices with low…
In this paper, we consider the problem of Robust Matrix Completion (RMC) where the goal is to recover a low-rank matrix by observing a small number of its entries out of which a few can be arbitrarily corrupted. We propose a simple…
Random bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require "strong" RBGs that produce high-entropy bit…
Randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information. This paper provides randomness extraction against quantum side information whose…
We present a simple and robust construction of a real-time quantum random number generator (QRNG). Our minimalist approach ensures stable operation of the device as well as its simple and straightforward hardware implementation as a…
We consider the problem of extracting entropy by sparse transformations, namely functions with a small number of overall input-output dependencies. In contrast to previous works, we seek extractors for essentially all the entropy without…
Information-efficient approaches for extracting randomness from imperfect sources have been extensively studied, but simpler and faster ones are required in the high-speed applications of random number generation. In this paper, we focus on…
Importance sampling based on quasi-probability decomposition is the backbone of many widely used techniques, such as error mitigation, circuit knitting, and, more generally, virtual quantum resource distillation, as it allows one to…
We present an algorithm that, with high probability, generates a random spanning tree from an edge-weighted undirected graph in $\tilde{O}(n^{4/3}m^{1/2}+n^{2})$ time (The $\tilde{O}(\cdot)$ notation hides $\operatorname{polylog}(n)$…