Related papers: Quantum Skew Divergence
We analyze two ways to obtain distinguishability measures between quantum maps by employing the square root of the quantum Jensen-Shannon divergence, which forms a true distance in the space of density operators. The arising measures are…
Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton…
We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…
A Gaussian quantum theory of bosonic modes has been widely used to describe quantum optical systems, including coherent Ising machines (CIMs) that consist of $\chi^{(2)}$ degenerate optical parametric oscillators (DOPOs) as nonlinear…
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual…
Hypothesis testing is a fundamental issue in statistical inference and has been a crucial element in the development of information sciences. The Chernoff bound gives the minimal Bayesian error probability when discriminating two hypotheses…
We consider the divergences in quantum electrodynamics. Our approach is based on ideas from the theory of generalized wave operators. In particular, we use the concept of the deviation factor. The deviation factor characterizes the…
We generalize the Jensen-Shannon divergence by considering a variational definition with respect to a generic mean extending thereby the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and…
In this work, we derive state-dependent uncertainty relations (uncertainty equalities) in which commutators of incompatible operators (not necessarily Hermitian) are explicitly present and state-independent uncertainty relations based on…
Unlike the classical smoothing theory, it is well known that quantum smoothers are, in general, not well--defined by the quantum conditional expectation. The purpose of this paper is to propose a new quantum smoothing theory based on the…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
Properties of random mixed states of order $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure, the trace distance between two random states…
We extend the concept of Wigner-Yanase-Dyson skew information to something we call ``metric adjusted skew information'' (of a state with respect to a conserved observable). This ``skew information'' is intended to be a non-negative quantity…
Bregman divergences generalize measures such as the squared Euclidean distance and the KL divergence, and arise throughout many areas of machine learning. In this paper, we focus on the problem of approximating an arbitrary Bregman…
Message identification (M-I) divergence is an important measure of the information distance between probability distributions, similar to Kullback-Leibler (K-L) and Renyi divergence. In fact, M-I divergence with a variable parameter can…
The multivariate extended skew-normal distribution allows for accommodating raw data which are skewed and heavy tailed, and has at least three appealing statistical properties, namely closure under conditioning, affine transformations, and…
The pace of evolution of physical systems is fundamentally constrained by quantum speed limits (QSL), which have found broad applications in quantum science and technology. We consider the speed of evolution for quantum systems undergoing…
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…
This note explores uncertainty inequalities for quantum analogues of the Fisher information including the Wigner-Yanase skew information, and their connection to the quantum Sobolev inequalities proved by the author in [Journal of…
The celebrated L\'evy--Khintchine theorem is a fundamental limiting law that describes the growth rate of the denominators of the convergents in the continued fraction expansion of a Lebesgue-typical real number. In a recent breakthrough,…