Related papers: From f-divergence to quantum quasi-entropies and t…
This paper gives an overview about particular quasi-entropies, generalized quantum covariances, quantum Fisher informations, skew-informations and their relations. The point is the dependence on operator monotone functions. It is proven…
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…
The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions…
Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's…
The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Matrix monotone functions and relative modular operators are used. The origin is the relative entropy and the f-divergence, monotone metrics, covariance…
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and…
We develop a rigorous framework for quantifying quantum coherence in finite-dimensional systems by applying the Schur-Horn majorization theorem to relate eigenvalue distributions and diagonal entries of density matrices. Building on this…
The main result in this article shows that the quantum $f$-divergence of two states is equal to the classical $f$-divergence of the corresponding Nussbaum-Szko{\l}a distributions. This provides a general framework for studying certain…
In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
We investigate how quantum coherence can be distributed among the several off-diagonal elements of an arbitrary density matrix. An easily computable quantity that captures this variability notion is proposed and it is argued that it…
This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory.…
We present a quantum version of the generalized $(h,\phi)$-entropies, introduced by Salicr\'u \textit{et al.} for the study of classical probability distributions. We establish their basic properties, and show that already known quantum…
We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…
Quantum generalizations of the Fisher information are important in quantum information science, with applications in high energy and condensed matter physics and in quantum estimation theory, machine learning, and optimization. One can…
By formulating the axioms of quantum mechanics, von Neumann also laid the foundations of a "quantum probability theory". As such, it is regarded a generalization of the "classical probability theory" due to Kolmogorov. Outside of quantum…