Related papers: Quantum Relative Lorenz Curves
Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a.…
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this…
A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation…
Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the system's quantum critical point. We show that the system's temperature is significantly suppressed due to both the entropy…
We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to…
Taking advantage of coherent light beams, we experimentally investigate the variancebased uncertainty relations and the optimal majorization uncertainty relation for the two-dimensional quantum mechanical system.Different from most of the…
We introduce a notion of majorization flow, and demonstrate it to be a powerful tool for deriving simple and universal proofs of continuity bounds for entropic functions relevant in information theory. In particular, for the case of the…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…
We present a quantum theory of distances along a curve, based on a linear line element that is equal to the operator square root of the quadratic metric of Riemannian geometry. Since the linear line element is an operator, we treat it…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
Adopting a resource theory framework of thermodynamics for quantum and nano systems pioneered by Janzing et al. [Int. J. Th. Phys. 39, 2717 (2000)], we formulate the cost in useful work of transforming one resource state into another as a…
We study thermalization within a quantum system with an enhanced capacity to store information. This system has been recently introduced to provide a prototype model of how a black hole processes and stores information. We perform a…
This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems, made up of microscopic particles, in terms of a small number of macroscopic quantities, such as…
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…
Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (a.k.a.…
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…
Recent research on the thermodynamic arrow of time, at the microscopic scale, has questioned the universality of its direction. Theoretical studies showed that quantum correlations can be used to revert the natural heat flow (from the hot…