Related papers: Analysing causal structures using Tsallis entropie…
Causal discovery algorithms allow for the inference of causal structures from probabilistic relations of random variables. A natural field for the application of this tool is quantum mechanics, where a long-standing debate about the role of…
Entanglement, a defining property of quantum mechanics in which two physical subsystems cannot be seen as independent entities, challenges our everyday experience and classical intuition. However, only such strong quantum correlations…
A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their…
We show that classical chaining bounds on the suprema of random processes in terms of entropy numbers can be systematically improved when the underlying set is convex: the entropy numbers need not be computed for the entire set, but only…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
The strength of classical correlations is subject to certain constraints, commonly known as Bell inequalities. Violation of these inequalities is the manifestation of nonlocality---displayed, in particular, by quantum mechanics, meaning…
The extraction of spatio-temporal coherence in high-dimensional, chaotic, non-linear dynamical systems, such as turbulent flows, remains a fundamental challenge in physics, mathematics and engineering. In this work, we employ Shannon…
Inferring the effect of interventions within complex systems is a fundamental problem of statistics. A widely studied approach employs structural causal models that postulate noisy functional relations among a set of interacting variables.…
We present universal relations between entanglement entropy, which quantifies the quantum correlation between subsystems, and the elastic cross section, which is the primary observable for high energy particle scattering, by employing a…
We investigate the classical limit of a type of semiclassical evolution, the pertinent system representing the interaction between matter and a given field. On using as a quantifier of the ensuing dynamics Tsallis q-entropy, we encounter…
Coherence is the most fundamental quantum feature of the nonclassical systems. The understanding of coherence within the resource theory has been attracting increasing interest among which the quantification of coherence is an essential…
We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…
A method of estimating the joint probability mass function of a pair of discrete random variables is described. This estimator is used to construct the conditional Shannon-R\'eyni-Tsallis entropies estimates. From there almost sure rates of…
It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…
We show that within classical statistical mechanics it is possible to naturally derive power law distributions which are of Tsallis type. The only assumption is that microcanonical distributions have to be separable from of the total system…
In this paper we formulate a kind of new geometric measure of quantum correlations. This new measure is in terms of the quantum Tsallis relative entropy and can be viewed as a one-parameter extension quantum discordlike measure that…
This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to…
Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the…