Related papers: Distributional property testing in a quantum world
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
The field of property testing of probability distributions, or distribution testing, aims to provide fast and (most likely) correct answers to questions pertaining to specific aspects of very large datasets. In this work, we consider a…
Randomness is a critical resource of modern cryptosystems. Quantum mechanics offers the best properties of an entropy source in terms of unpredictability. However, these sources are often fragile and can fail silently. Therefore,…
We initiate a systematic investigation of distribution testing in the framework of algorithmic replicability. Specifically, given independent samples from a collection of probability distributions, the goal is to characterize the sample…
Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
In this paper, we consider the problem of testing properties of joint distributions under the Conditional Sampling framework. In the standard sampling model, the sample complexity of testing properties of joint distributions is exponential…
Deep neural networks have established themselves as one of the most promising machine learning techniques. Training such models at large scales is often parallelized, giving rise to the concept of distributed deep learning. Distributed…
We initiate the study of quantum property testing in sparse directed graphs, and more particularly in the unidirectional model, where the algorithm is allowed to query only the outgoing edges of a vertex. In the classical unidirectional…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
Quantum computing is presently undergoing rapid development to achieve a significant speedup promised in certain applications. Nonetheless, scaling quantum computers remains a formidable engineering challenge, prompting exploration of…
In the near future, there will likely be special-purpose quantum computers with 40-50 high-quality qubits. This paper lays general theoretical foundations for how to use such devices to demonstrate "quantum supremacy": that is, a clear…
In practical situations, the reliability of quantum resources can be compromised due to complex generation processes or adversarial manipulations during transmission. Consequently, the trials generated sequentially in an experiment may…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
It is known in the context of decentralised control that there exist control strategies consistent with the requirements of a given information structure, yet physically unimplementable through any amount of passive common randomness. This…
We study from a theoretical viewpoint the fundamental problem of efficiently computing the stationary distribution of general classes of structured Markov processes. In strong contrast with previous work, we consider this fundamental…