Related papers: Semi-Quantitative Group Testing: A Unifying Framew…
This article reviews a class of adaptive group testing procedures that operate under a probabilistic model assumption as follows. Consider a set of $N$ items, where item $i$ has the probability $p$ ($p_i$ in the generalized group testing)…
The main goal of group testing with inhibitors (GTI) is to efficiently identify a small number of defective items and inhibitor items in a large set of items. A test on a subset of items is positive if the subset satisfies some specific…
In the Group Testing problem, the objective is to learn a subset K of some much larger domain N, using the shortest-possible sequence of queries Q. A feedback to a query provides some information about the intersection between the query and…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…
Group testing is utilized in the case when we want to find a few defectives among large amount of items. Testing n items one by one requires n tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the…
Semi-quantum key distribution (SQKD) protocols attempt to establish a shared secret key between users, secure against computationally unbounded adversaries. Unlike standard quantum key distribution protocols, SQKD protocols contain at least…
Characterization of experimental systems is an essential step in developing and improving quantum hardware. A collection of protocols known as Randomized Benchmarking (RB) was developed in the past decade, which provides an efficient way to…
In the problem of classical group testing one aims to identify a small subset (of size $d$) diseased individuals/defective items in a large population (of size $n$). This process is based on a minimal number of suitably-designed group tests…
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of possibly-noisy tests, and is relevant in applications such as medical testing, communication protocols, pattern…
An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…
Semi-quantum key distribution protocols are designed to allow two parties to establish a shared secret key, secure against an all-powerful adversary, even when one of the users is restricted to measuring and preparing quantum states in one…
Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find…
The goal of the group testing problem is to identify a set of defective items within a larger set of items, using suitably-designed tests whose outcomes indicate whether any defective item is present. In this paper, we study how the number…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
A numerical semigroup is a co-finite submonoid of the monoid of non-negative integers under addition. Many properties of numerical semigroups rely on some fundamental invariants, such as, among others, the set of gaps (and its cardinality),…
Testing a global null is a canonical problem in statistics and has a wide range of applications. In view of the fact that no uniformly most powerful test exists, prior and/or domain knowledge are commonly used to focus on a certain class of…
In the group testing problem the aim is to identify a small set of $k\sim n^\theta$ infected individuals out of a population size $n$, $0<\theta<1$. We avail ourselves of a test procedure capable of testing groups of individuals, with the…
We consider a zero-error probabilistic group testing problem where individuals are defective independently but not with identical probabilities. We propose a greedy set formation method to build sets of individuals to be tested together. We…
Detection of defective members of large populations has been widely studied in the statistics community under the name "group testing", a problem which dates back to World War II when it was suggested for syphilis screening. There the main…