Related papers: Tilted Hardy paradoxes for device-independent rand…
We prove that as conjectured by Ac\'{\i}n et al. [Phys. Rev. A 93, 040102(R) (2016)], two bits of randomness can be certified in a device-independent way from one bit of entanglement using the maximal quantum violation of Gisin's elegant…
Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for…
Particularly in genomics, but also in other fields, it has become commonplace to undertake highly multiple Student's $t$-tests based on relatively small sample sizes. The literature on this topic is continually expanding, but the main…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the…
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,…
Quantum random number generators (QRNGs) harness the inherent unpredictability of quantum mechanics to produce true randomness. Yet, in many optical implementations, the light source remains a potential vulnerability - susceptible to…
We Haar uniformly generate random states of various ranks and study their performance in an entanglement-based quantum key distribution (QKD) task. In particular, we analyze the efficacy of random two-qubit states in realizing…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
We show two experimental realizations of Hardy ladder test of quantum nonlocality using energy-time correlated photons, following the scheme proposed by A. Cabello \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 040401 (2009)]. Unlike,…
Device-independent quantum key distribution (DIQKD) promises cryptographic security based solely on observed quantum correlations, yet its implementation over long distances remains limited. Routed Bell tests have recently re-emerged as a…
This paper investigates Distributed Hypothesis testing (DHT), in which a source $\mathbf{X}$ is encoded given that side information $\mathbf{Y}$ is available at the decoder only. Based on the received coded data, the receiver aims to decide…
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…
Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…
This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the \emph{expected} rate of the sensor-detector link is constrained. Unlike for the well-known…
Device-independent (DI) cryptography represents the highest level of security, enabling cryptographic primitives to be executed safely on uncharacterized devices. Moreover, with successful proof-of-concept demonstrations in randomness…
Random number generators play an essential role in cryptography and key distribution. It is thus important to verify whether the random numbers generated from these devices are genuine and unpredictable by any adversary. Recently, quantum…
Study of nonlocal correlations in term of Hardy's argument has been quite popular in quantum mechanics. Recently Hardy's argument of non-locality has been studied in the context of generalized non-signaling theory as well as theory…
We study hypothesis testing (aka state certification) in the non-identically distributed setting. A recent work (Garg et al. 2023) considered the classical case, in which one is given (independent) samples from $T$ unknown probability…
We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional…