Interpolation for completely positive maps: numerical solutions

TL;DR

This paper introduces numerical techniques, including semidefinite programming and convex minimization, for constructing completely positive maps between matrix algebras that match specified data.

Contribution

It provides new computational methods for finding completely positive maps with prescribed values, supported by practical numerical examples.

Findings

Semidefinite programming effectively finds completely positive maps.

Convex minimization offers an alternative computational approach.

Numerical examples demonstrate the methods' applicability.

Abstract

We present certain techniques to find completely positive maps between matrix algebras that take prescribed values on given data. To this aim we describe a semidefinite programming approach and another convex minimization method supported by a numerical example.