Related papers: An optimal problem for relative entropy
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically…
The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts and then measure the joint…
Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables.
In this paper we deal with two quantum relative entropy preserver problems on the cones of positive (either positive definite or positive semidefinite) operators. The first one is related to a quantum R\'enyi relative entropy like quantity…
Let $A$ and $B$ be two accretive operators. We first introduce the weighted geometric mean of $A$ and $B$ together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of $A$ and $B$. The…
Let ${X_1,...,X_n}$ be i.i.d. random observations. Let $\mathbb{S}=\mathbb{L}+\mathbb{T}$ be a $U$-statistic of order $k\ge2$ where $\mathbb{L}$ is a linear statistic having asymptotic normal distribution, and $\mathbb{T}$ is a…
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this…
In this paper, we discuss an application of the SDDP type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse…
A classical upper bound for quantum entropy is identified and illustrated, $0\leq S_q \leq \ln (e \sigma^2 / 2\hbar)$, involving the variance $\sigma^2$ in phase space of the classical limit distribution of a given system. A fortiori, this…
The Esscher Transform is a tool of broad utility in various domains of applied probability. It provides the solution to a constrained minimum relative entropy optimization problem. In this work, we study the generalization of the Esscher…
The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…
We derive an optimal entropic uncertainty relation for an arbitrary pair of observables in a two-dimensional Hilbert space. Such a result, for the simple case we are considering, definitively improves all the entropic uncertainty relations…
We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X in R^n in a polyhedron P in R^n, by solving a certain entropy maximization…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
We consider the \emph{two-dimensional range maximum query (2D-RMQ)} problem: given an array $A$ of ordered values, to pre-process it so that we can find the position of the smallest element in the sub-matrix defined by a (user-specified)…
The Tsallis relative entropy $S_q (\hat{\rho},\hat{\sigma})$ measures the distance between two arbitrary density matrices $\hat{\rho}$ and $\hat{\sigma}$. In this work the approximation to this quantity when $q=1+\delta$ ($\delta\ll 1$) is…
We provide optimal measurement schemes for estimating relative parameters of the quantum state of a pair of spin systems. We prove that the optimal measurements are joint measurements on the pair of systems, meaning that they cannot be…
Consider the following variant of the set cover problem. We are given a universe $U=\{1,...,n\}$ and a collection of subsets $\mathcal{C} = \{S_1,...,S_m\}$ where $S_i \subseteq U$. For every element $u \in U$ we need to find a set $\phi(u)…