Related papers: Purity results for some arithmetically defined mea…
In this work we study the properties of an purification-based entropic metric for measuring the distance between both quantum states and quantum processes. This metric is defined as the square root of the entropy of the average of two…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
We introduce a continuous time model of many-body quantum dynamics based on infinitesimal random unitary operations, combined with projective measurements. We consider purification dynamics in this model, where the system is initialized in…
A series of frequent measurements on a quantum system (Zeno-like measurements) is shown to result in the ``purification'' of another quantum system in interaction with the former. Even though the measurements are performed on the former…
We find sufficient conditions for bounded density shifts to have a unique measure of maximal entropy. We also prove that every measure of maximal entropy of a bounded density shift is fully supported. As a consequence of this, we obtain…
We construct the entropic measure $\mathbb{P}^\beta$ on compact manifolds of any dimension. It is defined as the push forward of the Dirichlet process (another random probability measure, well-known to exist on spaces of any dimension)…
We consider qubit purification under simultaneous continuous measurement of the three non-commuting qubit operators \sigma_x, \sigma_y, \sigma_z. The purification dynamics is quantified by (i) the average purification rate, and (ii) the…
We present a systematic study of the purity for Gaussian states of single-mode continuous variable systems. We prove the connection of purity to observable quantities for these states, and show that the joint measurement of two conjugate…
We present methods for evaluating the rate of change in quantities during quantum evolution due to coupling to the environment (dissipation hereafter). The protocol is based on repeating a given quantum circuit (or quantum operation) twice,…
We present optimal and minimal measurements on identical copies of an unknown state of a qubit when the quality of measuring strategies is quantified with the gain of information (Kullback of probability distributions). We also show that…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
In this paper we study ergodic theory of countable Markov shifts. These are dynamical systems defined over non-compact spaces. Our main result relates the escape of mass, the measure theoretic entropy, and the entropy at infinity of the…
Continuous monitoring of an otherwise closed quantum system has been found to lead to a measurement-induced phase transition (MIPT) characterized by abrupt changes in the entanglement or purity of the many-body quantum state. For an…
We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight H\"older-behavior for this operation under minimal assumptions. Our…
Purification is a process in which decoherence is partially reversed by using several input systems which have been subject to the same noise. The purity of the outputs generally increases with the number of input systems, and decreases…
We establish arithmeticity in the sense of A. Katok and F. Rodriguez Hertz of smooth actions $\alpha$ of $\mathbb{R}^k$ on an anonymous manifold $M$ of dimension $2k+1$ provided that there is an ergodic invariant Borel probability measure…
Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information…
Given an irreducible subshift of finite type X, a subshift Y, a factor map \pi : X \to Y, and an ergodic invariant measure \nu on Y, there can exist more than one ergodic measure on X which projects to \nu and has maximal entropy among all…