Related papers: The Infinite-Dimensional Quantum Entropy: the Unif…
In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of…
This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with…
In sharp contrast to the corresponding classical systems cases it is not yet understood how to define a mechanical quantity with the interpretation of entropy creation rate for nonequilibrum stationary states of finite quantum systems with…
The recent article "Entropic Updating of Probability and Density Matrices" [1] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative…
By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described…
We propose a novel family of entanglement measures for time-separated subsystems. Our definitions are applicable to any quantum system, continuous or discrete. To illustrate their utility, we derive upper and lower bounds on time-separated…
Quantum entanglements, describing truly quantum couplings, are stu died and classified from the point of view of quantum compound states. We show that c lassical-quantum correspondences such as quantum encodings can be treated as…
Entanglement entropy is one of the most prominent measures in quantum physics. We show that it has an interesting ergotropic interpretation in terms of unitarily extracted work. It determines how much energy one can extract from a source of…
The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated…
We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a…
This paper studies the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspace. Upper bounds of these entropy numbers in the uniform norm are obtained and applied…
We show that the extended Bloch representation of quantum mechanics also applies to infinite-dimensional entities, to the extent that the number of (possibly infinitely degenerate) outcomes of a measurement remains finite, which is always…
We propose the use of a gravitational uncertainty principle for gravitation. We define the corresponding gravitational Planck's constant and the gravitational quantum of mass. We define entropy in terms of the quantum of gravity with the…
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and…
We discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to…
Fluctuation theorems provide universal constraints on nonequilibrium energy and entropy fluctuations, making them a natural framework to assess how and to what extent quantum resources become thermodynamically relevant. We develop a unified…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
In the course of the last decades entropic uncertainty relations have attracted much attention not only due to their fundamental role as manifestation of non-classicality of quantum mechanics, but also as major tools for applications of…