A decomposition theorem for positive maps, and the projection onto a spin factor

TL;DR

This paper proves a decomposition theorem for positive maps between matrix algebras, showing they can be expressed as a sum of a maximal decomposable map and an atomic map, with detailed analysis for projections onto spin factors.

Contribution

It introduces a new decomposition theorem for positive maps and analyzes the positive projection onto spin factors, advancing understanding in operator algebra theory.

Findings

Positive maps decompose into maximal decomposable and atomic parts.

The decomposition is unique and optimal.

Detailed analysis of projections onto spin factors.

Abstract

It is shown that each positive map between matrix algebras is the sum of a maximal decomposable map and an atomic map which is both optimal and co-optimal. The result is analyzed in detail for the positive projection onto a spin factor.