Related papers: Invariance entropy for uncertain control systems

We examine the conjecture that entropy production in subsystems of a given system can be used as a dynamical criterion for quantum chaos in the latter. Numerical results are presented for finite dimensional spin systems as also for the…

Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability…

Envariance, or environment-assisted invariance, is a recently identified symmetry for maximally entangled states in quantum theory with important ramifications for quantum measurement, specifically for understanding Born's rule. We…

We connect two recent advances in the stochastic analysis of nonequilibrium systems: the (loose) uncertainty principle for the currents, which states that statistical errors are bounded by thermodynamic dissipation; and the analysis of…

We present a series of statements about scaling entropy, a metric invariant of dynamical systems proposed by A. M. Vershik in the late 90's. We show that it is a metric invariant indeed and calculate it in several special cases.

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…

Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…

Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…

Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…

Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…

Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…

In this work, we study the slow entropy type invariant of a dynamical system proposed by A. M. Vershik. We provide an explicit construction of a system whose class of scaling entropy sequences is empty. For this unstable case, we introduce…

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly…

We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…

This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…

Uncertainty reduction is vital for improving system reliability and reducing risks. To identify the best target for uncertainty reduction, uncertainty importance measure is commonly used to prioritize the significance of input variable…

In 2002, Krishna and Parthasarathy [\textit{Sankhy\={a} Ser. A}] derived discrete quantum version of Maassen-Uffink [\textit{Phys. Rev. Lett., 1988}] entropic uncertainty principle. In this paper, using the notion of continuous…

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K,Q). If the stable subgroup of the uncontrolled system is closed and K has positive…

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the…