Determination of the noise parameters in a one-dimensional open quantum system

TL;DR

This paper models a one-dimensional open quantum system with noise affecting an impurity's spin, deriving transmission/reflection probabilities and highlighting the importance of complete positivity for physical validity.

Contribution

It provides explicit expressions for noise parameters in a quantum system and demonstrates the necessity of complete positivity for physical consistency.

Findings

Derived transmission and reflection probabilities in noisy quantum systems

Showed that non-completely positive maps can produce unphysical negative probabilities

Highlighted the importance of complete positivity in quantum noise modeling

Abstract

We consider an electron magnetically interacting with a spin-1/2 impurity, embedded in an external environment whose noisy term acts only on the impurity's spin, and we find expressions for the electron transmission and reflection probabilities in terms of the phenomenological noise parameters. Moreover, we give a simple example of the necessity of complete positivity for physical consistency, showing that a positive but not completely positive dissipative map can lead to negative transmission probabilities.