Structural Decomposition for Quantum Two-level Systems

TL;DR

This paper introduces a novel input-output modeling approach for two-level quantum systems, enabling analysis of properties like decoherence-free subspaces and quantum measurements through controllability and observability concepts.

Contribution

It develops explicit coordinate transformations for quantum systems, facilitating the study of their steady states, decoherence, and measurement properties, extending classical control concepts to quantum systems.

Findings

Explicit rotation matrices for model transformation

Analysis of steady-state solutions and decoherence-free subspaces

Application to quantum back-action evading measurements

Abstract

An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of quantum linear systems. By means of the notions of controllability and observability, coordinate transformations, which are rotation matrices, can be constructed explicitly that transform an input-output model to a new one. The new input-output model enables us to investigate many interesting properties of the two-level quantum system, such as steady-state solutions to the Lindblad master equation, quantum decoherence-free (DF) subspaces, quantum non-demolition (QND) variables, and the realization of quantum back-action evading (BAE) measurements. The physical system in (Wang, J. \& Wiseman, H. M. (2001), Feedback-stabilization of an arbitrary pure state of a two-level atom, Physical Review A 64(6), 063810) is re-studied to illustrate the results presented in this paper.