Related papers: Quantum conditional entropy for infinite-dimension…
We show how to use properties of the quantum conditional mutual information to obtain continuity bounds for information characteristics of quantum channels depending on their input dimension. First we prove tight estimates for variation of…
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…
We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic…
We study dynamical systems with the property that all the nontrivial factors have infinite topological entropy (or, positive mean dimension). We establish an ``if and only if'' condition for this property among a typical class of dynamical…
The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to…
In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied…
Two types of information entropy are studied for the quantum states of a model for the matter core inside a black hole geometry. A detailed description is first given of the quantum mechanical picture leading to a spectrum of bound states…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…
What are the conditions on a field theoretic model leading to a finite entanglement entropy density? We prove two very general results: 1) Ultraviolet finiteness of a theory does not guarantee finiteness of the entropy density; 2) If the…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
The most fundamental properties of quantum entropy are derived by considering the union of two ensembles. We discuss the limits these properties put on an entropy measure and obtain that they uniquely determine the form of the entropy…
Quantum uncertainty relations are typically analyzed for a pair of incompatible observables, however, the concept per se naturally extends to situations of more than two observables. In this work, we obtain tripartite quantum…
The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should…
One of the defining traits of quantum mechanics is the uncertainty principle which was originally expressed in terms of the standard deviation of two observables. Alternatively, it can be formulated using entropic measures, and can also be…
Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining…
In this paper we will give a short presentation of the quantum Levy-Khinchin formula and of the formulation of quantum continual measurements based on stochastic differential equations, matters which we had the pleasure to work on in…
We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in…
What would be a reasonable definition of the conditional entropy of bipartite quantum processes, and what novel insight would it provide? We develop this notion using four information-theoretic axioms and define the corresponding…
In this paper we derive a new quantum entropic uncertainty relation, bounding the conditional smooth quantum min entropy based on the result of a measurement using a two outcome POVM and the failure probability of a classical sampling…