Stability property for the quantum jump operators of an open system

TL;DR

This paper proves the continuity of spectral gaps and related constants for Lindblad generators in finite-dimensional open quantum systems, using bimodule structures and techniques from operator theory, with applications to quantum optics.

Contribution

It introduces a method to analyze the stability of spectral gaps and quantum-classical distinctions in open quantum systems via bimodule structures.

Findings

Spectral gaps are continuous with respect to jump operators.

Complete Logarithmic constants vary continuously in the Lindblad framework.

The $g^2(0)$ constant's continuity helps distinguish quantum from classical light.

Abstract

We show the continuity property of spectral gaps and complete Logarithmic constants in terms of the jump operators of Lindblad generators in finite dimensional setting. Our method is based on the bimodule structure of the derivation space and the technique developed in [Paulsen09]. Using the same trick, we also show the continuity of the $g^2(0)$ constant used to distinguish quantum and classical lights in quantum optics.