Decoherence and the conditions for the classical control of quantum systems

TL;DR

This paper identifies the conditions under which a quantum system can act as a classical controller for another quantum system, emphasizing the role of decoherence and rapid diagonalisation.

Contribution

It establishes that a quantum controller must be an open, rapidly diagonalised system to function as a classical controller, linking decoherence to classical control conditions.

Findings

Controller must be an open system

Rapid diagonalisation induces decoherence

Example with quantum optomechanical control

Abstract

We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalised in the basis of the controller variable that is coupled to the controlled system. This causes decoherence in the controlled system that can be made small if the rate of diagonalisation is fast. We give a detailed example based on the quantum optomechanical control of a mechanical resonator. The resulting equations are similar in structure to recently proposed models for consistently combining quantum and classical stochastic dynamics.