Related papers: Beyond Hoeffding and Chernoff: Trading conclusiven…
Hypothesis exclusion is an information-theoretic task in which an experimenter aims at ruling out a false hypothesis from a finite set of known candidates, and an error occurs if and only if the hypothesis being ruled out is the ground…
We prove the converse part of the theorem for quantum Hoeffding bound on the asymptotics of quantum hypothesis testing, essentially based on an argument developed by Nussbaum and Szkola in proving the converse part of the quantum Chernoff…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
Quantum state exclusion is an operational task with application to ontological interpretations of quantum states. In such a task, one is given a system whose state is randomly selected from a finite set, and the goal is to identify a state…
Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive…
The concept of antidistinguishability of quantum states has been studied to investigate foundational questions in quantum mechanics. It is also called quantum state elimination, because the goal of such a protocol is to guess which state,…
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous…
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
One of the fundamental tenets of quantum mechanics is that non-orthogonal states cannot be distinguished perfectly. When distinguishing multiple copies of a mixed quantum state, a collective measurement, which generates entanglement between…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szko{\l}a mapping. The lower bound provides a…
In this paper we present the solution to the problem of optimally discriminating among quantum states, i.e., identifying the states with maximum probability of success when a certain fixed rate of inconclusive answers is allowed. By varying…
This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
Quantum hypothesis testing is a central task in the entire field of quantum information theory. Understanding its ultimate limits will give insight into a wide range of quantum protocols and applications, from sensing to communication.…
This work is devoted to explore fundamental aspects of the spectral properties of few-body general operators. We first consider the following question: when we know the probability distributions of a set of observables, what can we way on…
Hoeffding's formulation and solution to the universal hypothesis testing (UHT) problem had a profound impact on many subsequent works dealing with asymmetric hypotheses. In this work, we introduce a quantum universal hypothesis testing…
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the optimal strategy that minimizes the total probability of error. This leads to the identification of the…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…
This paper develops an optimal Chernoff type bound for the probabilities of large deviations of sums $\sum_{k=1}^n f (X_k)$ where $f$ is a real-valued function and $(X_k)_{k \in \mathbb{Z}_{\ge 0}}$ is a finite state Markov chain with an…