A Kernel Approach to the Stinespring and Kraus Representations

TL;DR

This paper introduces a kernel-based method to derive the Stinespring and Kraus theorems, providing a new perspective on the structure of completely positive maps in quantum information theory.

Contribution

It offers a self-contained derivation of key theorems using scalar positive-definite kernels, simplifying and unifying the understanding of completely positive maps.

Findings

Provides a novel kernel-based derivation of the Stinespring theorem.

Unifies the Kraus and Stinespring representations through kernel methods.

Simplifies the mathematical framework for completely positive maps.

Abstract

We give a self-contained derivation of the Stinespring and Kraus structure theorems for completely positive maps using only scalar positive-definite kernels.