Related papers: A brief introduction to observational entropy
We develop a notion of quantum observable for the general boundary formulation of quantum theory. This notion is adapted to spacetime regions rather than to hypersurfaces and naturally fits into the topological quantum field theory like…
The entropy definition is deduced by means of (re)deriving the generalized non-linear Langevin equation using Zwanzig projector operator formalism. It is shown to be necessarily related to an invariant measure which, in classical mechanics,…
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…
We consider an arbitrary quantum system coupled non perturbatively to a large arbitrary and fully quantum environment. In [G. Ithier and F. Benaych-Georges, Phys. Rev. A 96, 012108 (2017)] the typicality of the dynamics of such an embedded…
The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's…
For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure.…
Existing literature on timed opacity uses specific definitions for restricted subclasses of timed automata or limited observation models. This lack of a unified definition makes it difficult to establish formal relationships and compare the…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
In ordinary Quantum Mechanics only ideally instantaneous observations of a quantity or a set of compatible quantities are usually considered. In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of…
We explore nonequilibrium features of certain operator algebras which appear in quantum gravity. The algebra of observables in a black hole background is a Type $\mathrm{II}_\infty$ von Neumann algebra. We discuss how this algebra can be…
By using relative entropy of coherence, we characterize the coherence gain induced by some quantum evolutions, including the cohering power of unitary operations and the decohering power of quantum operations. We find that the cohering…
We introduce a theory of quantum resource degradation grounded in a decomposition of observational entropy, which partitions the total resource into inter-block coherence ($\mathcal{C}_{\text{rel}}$) and intra-block noise…
An information theory description of finite systems explicitly evolving in time is presented for classical as well as quantum mechanics. We impose a variational principle on the Shannon entropy at a given time while the constraints are set…
New formulations of quantum generalized fluctuation-dissipation relations in terms of characteristic and probabilistic functionals of continuous observations are suggested and discussed. It is shown that control of entropy production in…
The role of time in quantum mechanics is discussed. The differences between ordinary observables and an observable which corresponds to the time of an event is examined. In particular, the time-of-arrival of a particle to a fixed location…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
This article consists of a very short introduction to classical and quantum information theory. Basic properties of the classical Shannon entropy and the quantum von Neumann entropy are described, along with related concepts such as…