Related papers: Minimal distance between random orbits
We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
In this paper, we study the asymptotic behavior of globally minimizing orbits of contact Hamiltonian systems. Under some assumptions, we prove that the $\omega$-limit set of globally minimizing orbits is contained in the set of semi-static…
Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…
Understanding distance metrics in high-dimensional spaces is crucial for various fields such as data analysis, machine learning, and optimization. The Manhattan distance, a fundamental metric in multi-dimensional settings, measures the…
This paper presents the asymptotic analysis of random lattices in high dimensions to clarify the distance properties of the considered lattices. These properties not only indicate the asymptotic value for the distance between any pair of…
We derive nearly tight and non-asymptotic convergence bounds for solutions of entropic semi-discrete optimal transport. These bounds quantify the stability of the dual solutions of the regularized problem (sometimes called Sinkhorn…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
The dynamics of entanglement between two - level atoms interacting with a common squeezed reservoir is investigated. It is shown that for spatially separated atoms there is a unique asymptotic state depending on the distance between the…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
The conventional Hamming distance measurement captures only the short-time dynamics of the displacement between the uncorrelated random configurations. The minimum difference technique introduced by Tirnakli and Lyra [Int. J. Mod. Phys. C…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…
Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from, e.g., imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare…
We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed of a central spin coupled and initially uncorrelated with…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated…
We consider the problem of distributing two conducting materials with a prescribed volume ratio in a given domain so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions. The gap between the two…
Recurrence quantification analysis is a method for measuring the complexity of dynamical systems. Recurrence determinism is a fundamental characteristic of it, closely related to correlation sum. In this paper, we study asymptotic behavior…