Related papers: Properties of Classical and Quantum Jensen-Shannon…
Sides and medians are both Jacobi coordinate magnitudes, moreover then equably entering the spherical coordinates on Kendall's shape sphere and the Hopf coordinates. This motivates treating medians on the same footing as sides in triangle…
Being the key resource in quantum physics, the proper quantification of coherence is of utmost importance. Amid complex-looking functionals in quantifying coherence, we set forth a simple and easy-to-evaluate approach: Principal diagonal…
Using Bloch's parametrization for qudits ($d$-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic $n$-qudit states as an Euclidean distance between two vectors of observables mean values in…
The main result of the paper is a construction of a five-parameter family of new bases in the algebra of symmetric functions. These bases are inhomogeneous and share many properties of systems of orthogonal polynomials on an interval of the…
In this note we compare two ways of measuring the $n$-dimensional "flatness" of a set $S\subset \mathbb{R}^d$, where $n\in \mathbb{N}$ and $d>n$. The first one is to consider the classical Reifenberg-flat numbers $\alpha(x,r)$ ($x \in S$,…
We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Leibler (KL) divergence, originally introduced in kinetic…
We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
Likelihood-free inference for simulator-based statistical models has recently attracted a surge of interest, both in the machine learning and statistics communities. The primary focus of these research fields has been to approximate the…
The Kullback-Leibler divergence or relative entropy is an information-theoretic measure between statistical models that play an important role in measuring a distance between random variables. In the study of complex systems, random fields…
Classically, Jensen's Inequality asserts that if $X$ is a compact convex set, and $f:K\to \mathbb{R}$ is a convex function, then for any probability measure $\mu$ on $K$, that $f(\text{bar}(\mu))\le \int f\;d\mu$, where $\text{bar}(\mu)$ is…
In this paper, we propose a novel Quantum Spacetime Theory (QST) that reinterprets spacetime as an emergent structure, challenging the traditional block universe paradigm and aligning with research into emergent spacetime. Using a sphere…
We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of…
The fidelity (Shannon mutual information between measurements and physical quantities) is proposed as a quantitative measure of the quality of physical measurements. The fidelity does not depend on the true value of unknown physical…
A small time delay between interactions, which has previously been shown to remove divergences from QED, is used to show that, if spacetime geometry is emergent from particle interactions in the manner suggested by Bondi, then Minkowski…
Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multi-point' kernels, and study their applications. We study a class of kernels based on Jensen type divergences and show that these…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
15 years ago Dmitry Diakonov wrote the paper "Towards lattice-regularized Quantum Gravity", arXiv:1109.0091. In his approach, gravity with metric and tetrads arise from pre-geometric quantum fields leading to unusual dimensions of physical…