Related papers: Jointly convex quantum Jensen divergences
Convex operational models (COMs) are considered as great extrapolations to larger settings of any statistical theory. In this article we generalize the maximum entropy principle (MaxEnt) of Jaynes' to any COM. After expressing Max-Ent in a…
We investigate how the type of Convexity of the Core function affects the Csisz\'{a}r $f$-divergence functional. A general treatment for the type of convexity has been considered and the associated perspective functions have been studied.…
The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by this connection to Convex Geometry, we survey various recent…
It is shown that, for open sets in classical potential theory and - more generally - for elliptic harmonic spaces, the set of Jensen measures for a point is a simple union of closed faces of a compact convex set which has been thoroughly…
We derive, for a bistochastic strictly contractive quantum channel on a matrix algebra, a relation between the contraction rate and the rate of entropy production. We also sketch some applications of our result to the statistical physics of…
The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of…
Some new inequalities of Karamata type are established with a convex function in this paper. The methods of our proof allow us to obtain an extended version of the reverse of Jensen inequality given by Pe{\v} cari\'c and Mi\'ci\'c. Applying…
We prove a matrix inequality for convex functions of a Hermitian matrix on a bipartite space. As an application we reprove and extend some theorems about eigenvalue asymptotics of Schr\"odinger operators with homogeneous potentials. The…
This is a contribution for the discussion on "A Gibbs sampler for a class of random convex polytopes" by Pierre E. Jacob, Ruobin Gong, Paul T. Edlefsen and Arthur P. Dempster to appear in the Journal of American Statistical Association.
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as…
We investigate $(0,1)$-matrices that are {\em convex}, which means that the ones are consecutive in every row and column. These matrices occur in discrete tomography. The notion of ranked essential sets, known for permutation matrices, is…
In this work, we explicitly compute the group inverse of symmetric and periodic Jacobi matrices.
Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
Jensen's inequality, attributed to Johan Jensen -- a Danish mathematician and engineer noted for his contributions to the theory of functions -- is a ubiquitous result in convex analysis, providing a fundamental lower bound for the…
A recent general model of entanglement, [5], that goes much beyond the usual one based on tensor products of vector spaces is further developed here. It is shown that the usual Cartesian product can be seen as two extreme particular…
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
In this paper we investigate the higher dimensional divergence functions of mapping class groups of surfaces and of CAT(0)--groups. We show that, for mapping class groups of surfaces, these functions exhibit phase transitions at the rank…