Complete positivity and self-adjointness

TL;DR

This paper characterizes the structure of symmetric completely positive operators and quantum Markov semigroup generators, providing new insights into their order structure and extreme points within certain contexts.

Contribution

It offers a detailed description of symmetric completely positive operators and quantum Markov semigroup generators, highlighting their structural properties and extremal elements.

Findings

Characterization of symmetric completely positive operators

Analysis of quantum Markov semigroup generators

New insights into order structure and extreme points

Abstract

We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family of inner products, also providing new information on the order strucure an extreme points in some previously studied cases.