Related papers: An axiomatic characterization of a two-parameter e…

An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…

In this letter, we give a concise, closed-form expression for the differential entropy of the sum of two independent, non-identically-distributed exponential random variables. The derivation is straightforward, but such a concise entropy…

The a-theorem is demonstrated for the RG flows of entanglement entropy in two and four dimensions. In four dimensions we relate it to the term quadratic in intrinsic derivative of the dilaton along the entangling surface in the dilaton…

Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…

We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various…

The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT)…

Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…

We present the modified relative entropy of entanglement for multi-party systems by a given relative density matrix which is spanned by a linear combination of the direct products of so-called basis of relative density matrices and reduced…

The second law of thermodynamics states that the entropy of an isolated system can only increase over time. This appears to conflict with the reversible evolution of isolated quantum systems under the Schr\"odinger equation, which preserves…

Properties of the max- relative entropy of entanglement are investigated, and its significance as an upper bound to the one shot rate for perfect entanglement dilution, under a particular class of quantum operations, is discussed. It is…

A criterion and necessary conditions for convergence (local continuity) of the quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of local continuity of the quantum…

We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the…

We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words at every level. As a consequence, we get that the subshifts…

We prove a theorem of uppersemicontinuity for the metric entropy of meromorphic maps.

We study the topological entropy of a two-parameter family of maps related to (a,b)-continued fraction algorithms and prove that it is constant on a square within the parameter space (two vertices of this square correspond to well-studied…

The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…

We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups, appropriately modifying existing notions of entropy. The basic properties of the algebraic entropy are given, as well as various examples. The main result of…

The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of…

It is shown that the laws of thermodynamics are extremely robust under generalizations of the form of entropy. Using the Bregman-type relative entropy, the Clausius inequality is proved to be always valid. This implies that thermodynamics…

Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a function of the…