Stabilizing Preparation of Quantum Gaussian States via Continuous Measurement

TL;DR

This paper introduces a continuous measurement-based method for stabilizing quantum Gaussian states, offering more flexible conditions and practical advantages over traditional dissipation-based approaches.

Contribution

It provides necessary and sufficient conditions for stabilization, including for imperfect measurements, enhancing the practical preparation of quantum Gaussian states.

Findings

Derived weaker stabilizing conditions than existing methods.

Provided parametric conditions for arbitrary pure Gaussian states.

Addressed stabilizing conditions under measurement inefficiency.

Abstract

This paper provides a stabilizing preparation method for quantum Gaussian states by utilizing continuous measurement. The stochastic evolution of the open quantum system is described in terms of the quantum stochastic master equation. We present necessary and sufficient conditions for the system to have a unique stabilizing steady Gaussian state. The conditions are much weaker than those existing results presented in the approach of preparing Gaussian states through environment engineering. Parametric conditions of how to prepare an arbitrary pure Gaussian state are provided. This approach provides more degrees of freedom to choose the system Hamiltonian and the system-environment coupling operators, as compared with the case where dissipation-induced approach is employed. The stabilizing conditions for the case of imperfect measurement efficiency are also presented. These results may benefit practical experimental implementation in preparing quantum Gaussian states.