Interaction free and decoherence free states

TL;DR

This paper derives the characteristic equations for states that are unaffected by interactions or decoherence in bipartite quantum systems, providing a unified framework for understanding interaction-free and decoherence-free states across various physical contexts.

Contribution

It introduces a general characteristic equation for states that remain unaffected by interactions or decoherence in bipartite systems governed by linear dynamics.

Findings

Derived the characteristic equation for interaction-free states.

Identified conditions for decoherence-free states in open systems.

Provided examples demonstrating the theory's applicability.

Abstract

An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical contexts.