相关论文: A minimax approach to one-shot entropy inequalitie…

The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…

We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic…

We consider two fundamental tasks in quantum information theory, data compression with quantum side information as well as randomness extraction against quantum side information. We characterize these tasks for general sources using…

Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected…

We study formal properties of smooth max-information, a generalization of von Neumann mutual information derived from the max-relative entropy. Recent work suggests that it is a useful quantity in one-shot channel coding, quantum rate…

The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of…

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

The variance of (relative) surprisal, also known as varentropy, so far mostly plays a role in information theory as quantifying the leading order corrections to asymptotic i.i.d.~limits. Here, we comprehensively study the use of it to…

In quantum Shannon theory, various kinds of quantum entropies are used to characterize the capacities of noisy physical systems. Among them, min-entropy and its smooth version attract wide interest especially in the field of quantum…

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…

Quantum information decoupling is a fundamental primitive in quantum information theory, underlying various applications in quantum physics. We prove a novel one-shot decoupling theorem formulated in terms of quantum relative entropy…

Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…

A fundamental tool to prove inner bounds in classical network information theory is the so-called conditional joint typicality lemma. In addition to the lemma, one often uses unions and intersections of typical sets in the inner bound…

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…

In this work, we propose a soft covering problem for fully quantum channels using relative entropy as a criterion for operator closeness. We establish covering lemmas by deriving one-shot bounds on the achievable rates in terms of smooth…

We introduce a new operational technique for deriving chain rules for general information theoretic quantities. This technique is very different from the popular (and in some cases fairly involved) methods like SDP formulation and operator…

Manipulation and quantification of quantum resources are fundamental problems in quantum physics. In the asymptotic limit, coherence distillation and dilution have been proposed by manipulating infinite identical copies of states. In the…

Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…