Related papers: Entropy functions and determinant inequalities

Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…

We introduce a simple geometrical construction similar to covariant holographic entanglement entropy but with the addition of a new term proportional to boundary region volume. This new procedure has properties strongly resembling classical…

This paper studies the problem of selecting a submatrix of a positive definite matrix in order to achieve a desired bound on the smallest eigenvalue of the submatrix. Maximizing this smallest eigenvalue has applications to selecting input…

We investigate structural properties of the completely positive semidefinite cone $\mathcal{CS}_+^n$, consisting of all the $n \times n$ symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This…

The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models…

Our aim is to provide a short and self contained synthesis which generalise and unify various related and unrelated works involving what we call Phi-Sobolev functional inequalities. Such inequalities related to Phi-entropies can be seen in…

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…

We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties,…

This paper is prepared as a contribution to the proceedings after the 12th ICSSUR/Feynfest Conference held in Foz do Iguacu (Brazil) from 2 to 6 May 2011. In the first part I briefy report the topic of entropic uncertainty relations for…

An information theory description of finite systems explicitly evolving in time is presented. We impose a MaxEnt variational principle on the Shannon entropy at a given time while the constraints are set at a former time. The resulting…

Strong and general entropic and geometric Heisenberg limits are obtained, for estimates of multiparameter unitary displacements in quantum metrology, such as the estimation of a magnetic field from the induced rotation of a probe state in…

The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a large class of random Laplacian matrices, this bound is essentially tight: the largest eigenvalue is, up to lower order terms,…

In this note, we present the determinant, the inverse and a lower bound for the smallest eigenvalue for some Hankel matrices

The data for many classification problems, such as pattern and speech recognition, follow mixture distributions. To quantify the optimum performance for classification tasks, the Shannon mutual information is a natural information-theoretic…

Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of…

The discrete power function on the hexagonal lattice proposed by Bobenko et al is considered, whose defining equations consist of three cross-ratio equations and a similarity constraint. We show that the defining equations are derived from…

Infinite determinantal measures introduced in this note are inductive limits of determinantal measures on an exhausting family of subsets of the phase space. Alternatively, an infinite determinantal measure can be described as a product of…

It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and…

We derive explicit expressions for the volume elements of both the minimal and maximal monotone metrics over the (n^{2} - 1)-dimensional convex set of n x n density matrices for the cases n = 3 and 4. We make further progress for the…

The nonnegative rank of a matrix A is the smallest integer r such that A can be written as the sum of r rank-one nonnegative matrices. The nonnegative rank has received a lot of attention recently due to its application in optimization,…