Related papers: Hermitian Maps: Approximations and Completely Posi…
In open quantum systems, it is known that if the system and environment are in a product state, the evolution of the system is given by a linear completely positive (CP) Hermitian map. CP maps are a subset of general linear Hermitian maps,…
We apply Hilbert module methods to show that normal completely positive maps admit weak tensor dilations. Appealing to a duality between weak tensor dilations and extensions of CP-maps, we get an existence proof for certain extensions. We…
We present a method for the determination of the completely positive (CP) map describing a physical device based on random preparation of the input states, random measurements at the output, and maximum-likelihood principle. In the…
We introduce the \emph{CP-distance} to quantify the deviation of Hermitian linear maps from complete positivity, defined as the minimal depolarizing noise required to render a map completely positive. We derive a closed spectral formula for…
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
Given an (anisotropic) Hermitian space $H$, the collection $P(H)$ of at most one-dimensional subspaces of $H$, equipped with the orthogonal relation $\perp$ and the zero linear subspace $\{0\}$, is a linear orthoset and up to…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…
We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…
We characterise absolutely dilatable completely positive maps on the space of all bounded operators on a Hilbert space that are also bimodular over a given von Neumann algebra as rotations by a suitable unitary on a larger Hilbert space…
One may ask which maps between Hilbert modules allow for a completely positive extension to a map acting block-wise between the associated (extended) linking algebras. In these notes we investigate in particular those of such CP-extendable…
We prove that proper pseudo-holomorphic maps between strictly pseudoconvex regions in almost complex manifolds extend to the boundary. The key point is that the Jacobian is far from zero near the boundary, and the proof is mainly based on…
A relation between values of a unitarily invariant norm of Hermitian operator before and after action of completely positive map is studied. If the norm is jointly defined on both the input and output Hilbert spaces, one defines a shrinking…
The description of the dynamics of an open quantum system in the presence of initial correlations with the environment needs different mathematical tools than the standard approach to reduced dynamics, which is based on the use of a…
A non-Hermitian complex symmetric 2x2 matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseux-expanded in terms…
We introduce the geometric mean and the parallel sum of completely positive (CP) maps on von Neumann algebras, based on the Pusz--Woronowicz theory of positive sesquilinear forms. We provide a concrete characterization via a block matrix…
We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones;…
The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix…
In this article we study different aspects of Hermitian operators applying the concept of positive decompositions. On the one hand, we characterize the positivity of an Hermitian operator by means of a norm condition where the factors of…
In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces $L^{2}(\mu)$, with $\mu$ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix to the…