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The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results…
Sinopoli et al. (TAC, 2004) considered the problem of optimal estimation for linear systems with Gaussian noise and intermittent observations, available according to a Bernoulli arrival process. They showed that there is a "critical"…
We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…
Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and…
In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal…
Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications…
We obtain analytical lower bounds on the concurrence of bipartite quantum systems in arbitrary dimensions related to the violation of separability conditions based on local uncertainty relations and on the Bloch representation of density…
Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients…
We show that, for any system with a number of levels which can be identified with n qubits, there is an inequality for the correlations between three compatible dichotomic measurements which must be satisfied by any noncontextual theory,…
A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to…
The aim of this paper is to discuss new results concerning some kinds of parametric extended entropies and divergences. As a result of our studies for mathematical properties on entropy and divergence, we give new bounds for the Tsallis…
We resolve a long-standing open question on the relationship between measure-theoretic dynamical complexity and symbolic complexity by establishing the exact word complexity at which measure-theoretic strong mixing manifests: For every…
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
It is shown here that symmetric hyperbolicity, which guarantees well-posedness, leads to a set of two inequalities for matrices whose elements are determined by a given theory. As a part of the calculation, carried out in a mostly-covariant…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…