Related papers: The Infinite-Dimensional Quantum Entropy: the Unif…
The prominent collective character of long-range interacting quantum systems makes them promising candidates for quantum technological applications. Yet, lack of additivity overthrows the traditional picture for entanglement scaling and…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
We show that the entanglement entropy of single quasiparticle excitations of one dimensional systems exceeds the ground state entanglement entropy for log(2), if the correlation length of the system is finite. For quadratic fermion systems…
A number of ideas and questions related to the construction of quantum processes are discussed. Quantum state extension, entanglement and asymptotic behaviour of the entropy are some of the issues explored. These topics are studied in more…
G\"oran Lindblad in 1983 published a monograph on non-equilibrium thermodynamics. We here summarize the contents of this book, and provide a perspective on its relation to later developments in statistical physics and quantum physics. We…
We sketch and emphasize the automatic emergence of a quantum potential Q in e.g. classical WDW type equations upon inserting a (Bohmian) complex wave function. The interpretation of Q in terms of momentum fluctuations via Fisher information…
The authors show that a wide class of Fredholm determinants arising in the representation theory of "big" groups such as the infinite-dimensional unitary group, solve Painleve equations. Their methods are based on the theory of integrable…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
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…
We review the derivation of quantum theory as an application of entropic methods of inference. The new contribution in this paper is a streamlined derivation of the Schr\"odinger equation based on a different choice of microstates and…
In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems and we introduce the notion of coefficient of quantum correlations. Our presentation stems from rigorous…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
We numerically analyze the dynamical generation of quantum entanglement in a system of 2 interacting particles, started in a coherent separable state, for decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy, computed at…
The concept of measurement is discussed. It is argued that counting process in mathematics is also measurement which requires a basic unit. The idea of scale is put forward. The basic unit itself, which are composed of the infinitesimal of…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings…
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…