Pure Gaussian state generation via dissipation: A quantum stochastic differential equation approach

TL;DR

This paper presents a QSDE-based framework for engineering dissipative Gaussian systems that generate pure states, clarifying their nullifier dynamics and providing practical implementation methods for quantum state transfer.

Contribution

It introduces a QSDE approach to characterize and implement pure Gaussian state generation via dissipation, offering new insights and practical methods.

Findings

Nullifier dynamics are passive in pure steady states

A general method for dissipative Gaussian system implementation

Clarification of environment's role in pure state stabilization

Abstract

Recently the complete characterization of a general Gaussian dissipative system having a unique pure steady state was obtained in [Koga and Yamamoto 2012, Phys. Rev. A 85, 022103]. This result provides a clear guideline for engineering an environment such that the dissipative system has a desired pure steady state such as a cluster state. In this paper, we describe the system in terms of a quantum stochastic differential equation (QSDE) so that the environment channels can be explicitly dealt with. Then a physical meaning of that characterization, which cannot be seen without the QSDE representation, is clarified; more specifically, the nullifier dynamics of any Gaussian system generating a unique pure steady state is passive. In addition, again based on the QSDE framework, we provide a general and practical method to implement a desired dissipative Gaussian system, which has a structure of quantum state transfer.