Decoherence-free linear quantum subsystems

TL;DR

This paper develops a comprehensive control-theoretic framework for identifying and constructing decoherence-free subsystems in infinite dimensional linear open quantum systems, enabling robust quantum information processing.

Contribution

It introduces a novel approach using controllability and observability concepts in the Heisenberg picture to characterize and construct decoherence-free subsystems.

Findings

Derived a necessary and sufficient condition for the existence of DF subsystems.

Provided explicit methods for constructing DF dynamics in specific examples.

Demonstrated coherent manipulation and preservation within DF subsystems.

Abstract

This paper provides a general theory for characterizing and constructing a decoherence-free (DF) subsystem for an infinite dimensional linear open quantum system. The main idea is that, based on the Heisenberg picture of the dynamics rather than the commonly-taken Schrodinger picture, the notions of controllability and observability in control theory are employed to characterize a DF subsystem. A particularly useful result is a general if and only if condition for a linear system to have a DF component; this condition is used to demonstrate how to actually construct a DF dynamics in some specific examples. It is also shown that, as in the finite dimensional case, we are able to do coherent manipulation and preservation of a state of a DF subsystem.