Related papers: Invariance entropy for uncertain control systems

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 study entropy--coherence relations near rank-deficient support boundaries in finite-dimensional quantum systems. For block-diagonal reference states, we establish support-sensitive coercivity estimates showing that the entropy cost of…

In communications, unknown variables are usually modelled as random variables, and concepts such as independence, entropy and information are defined in terms of the underlying probability distributions. In contrast, control theory often…

We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples include observations on sequential expanding maps,…

The folding entropy is a quantity originally proposed by Ruelle in 1996 during the study of entropy production in the non-equilibrium statistical mechanics. As derived through a limiting process to the non-equilibrium steady state, the…

The problem of estimating certain distributions over $\{0,1\}^d$ is considered here. The distribution represents a quantum system of $d$ qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is…

Uncertainty relation usually is one of the most important features in quantum mechanics, and is the backbone of quantum theory, which distinguishes from the rule in classical counterpart. Specifically, entropy-based uncertainty relations…

The objective of the consistent-amplitude approach to quantum theory has been to justify the mathematical formalism on the basis of three main assumptions: the first defines the subject matter, the second introduces amplitudes as the tools…

A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…

We propose a method for inferring entropy production (EP) in high-dimensional stochastic systems, including many-body systems and non-Markovian systems with long memory. Standard techniques for estimating EP become intractable in such…

A non-vanishing entropy production rate is one of the defining characteristics of any non-equilibrium system, and several techniques exist to determine this quantity directly from experimental data. The short-time inference scheme, derived…

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

Entropy production is a fundamental concept that plays a crucial role in the second law of thermodynamics and the measure of irreversibility. It imposes rigorous constraints on the kinds of transformations allowed in thermodynamic…

The uncertainty principle is an inherent characteristic of quantum mechanics. This principle can be formulated in various form. Fundamentally, this principle can be expressed in terms of the standard deviation of the measured observables.…

Coherent states (CS) quantum entropy can be split into two components. The dynamical entropy is linked with the dynamical properties of a quantum system. The measurement entropy, which tends to zero in the semiclassical limit, describes the…

The purpose of this note is to establish a connection between the problem of reliability (when there is an intermittent control-input channel failure that may occur between actuators, controllers and/or sensors in the system) and the notion…

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…

Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining…

The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…

Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…