Related papers: Completely positive mappings and mean matrices
For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…
We prove the existence of gaps between all the different classes of matrix monotone functions defined on an interval, provided the interval is non trivial and different from the whole real line. We then show how matrix monotone functions…
The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as…
This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension…
We present certain existence criteria and parameterisations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to…
In this note, we discuss dilation-theoretic matrix parametrizations of contractions and positive matrices. These parametrizations are then applied to some problems in quantum information theory. First we establish some properties of…
A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of…
We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is…
In this paper, we consider matrices whose entries are combinatorial sequences which can be expressed in terms of a convolution of elementary and complete homogeneous symmetric functions. We establish the total positivity of these matrices…
We classify all functions which, when applied term by term, leave invariant the sequences of moments of positive measures on the real line. Rather unexpectedly, these functions are built of absolutely monotonic components, or reflections of…
The Leinster matrix corresponding to a finite category has entries counting the number of morphisms between objects. A first question is to know which positive integer matrices come from at least one finite category. Here, that question…
In this article, a necessary and sufficient condition and a necessary condition are established for a function involving the gamma function to be logarithmically completely monotonic on $(0,\infty)$. As applications of the necessary and…
We give several new characterizations of completely monotone functions and Bernstein functions via two approaches: the first one is driven algebraically via elementary preserving mappings and the second one is developed in terms of the…
In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete…
In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of…
All beta-type functions, which are p-homogeneous, are determined. Applying this result, we show that a beta-type function is a homogeneous mean iff it is the harmonic one. A reformulation of a result due to Heuvers in terms of a Cauchy…
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is epsilon-far from having that property. The performance of the algorithm is judged by how many calls need to be made to…
In this paper the geometric mean of partial positive definite matrices with missing entries is considered. The weighted geometric mean of two sets of positive matrices is defined, and we show whether such a geometric mean holds certain…
We present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.
We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…