Fixed Space of Positive Trace-Preserving Super-Operators

TL;DR

This paper characterizes the structure of the fixed space of positive trace-preserving super-operators, providing insights that lead to an alternative proof of the fixed space of completely positive trace-preserving super-operators.

Contribution

It offers a detailed structural description of the fixed space of positive trace-preserving super-operators and an alternative proof for the complete characterization of the fixed space of completely positive trace-preserving super-operators.

Findings

Describes the structure of the fixed space of positive trace-preserving super-operators.

Provides an explicit form of the projection onto the fixed space.

Offers an alternative proof for the fixed space of completely positive trace-preserving super-operators.

Abstract

We examine the fixed space of positive trace-preserving super-operators. We describe a specific structure that this space must have and what the projection onto it must look like. We show how these results, in turn, lead to an alternative proof of the complete characterization of the fixed space of completely positive trace-preserving super-operators.