Related papers: Entropy Concentration and Universal Typicality for…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…
The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their work is that of local quantum…
We derive a lower bound on the smallest output entropy that can be achieved via vector quantization of a $d$-dimensional source with given expected $r$th-power distortion. Specialized to the one-dimensional case, and in the limit of…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
The characterization of irreversibility in general quantum processes is an open problem of increasing techno- logical relevance. Yet, the tools currently available to this aim are mostly limited to the assessment of dynamics induced by…
The idea of exploiting maximally-entangled states as a resource lies at the core of several modalities of quantum information processing, including secure quantum communication, quantum computation, and quantum sensing. However, due to…
We define a large class of quantum sources and prove a quantum analog of the asymptotic equipartition property. Our proof relies on using local measurements on the quantum source to obtain an associated classical source. The classical…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
This thesis addresses problems in the field of quantum information theory. The first part of the thesis is opened with concrete definitions of general quantum source models and their compression, and each subsequent chapter addresses the…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
We give a characterization of Maximum Entropy/Minimum Relative Entropy inference by providing two `strong entropy concentration' theorems. These theorems unify and generalize Jaynes' `concentration phenomenon' and Van Campenhout and Cover's…
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 pure quantum entanglement is generalized to the case of mixed compound states on an operator algebra to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized by quantum…
The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of compressible complete Euler system in the full space $ \mathbb{R}^d,\; d=2,3 $ is a weak solution of the system then eventually the…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…