Power Spectrum Identification for Quantum Linear Systems

TL;DR

This paper explores how to identify parameters and reconstruct quantum linear systems from their output power spectrum, which encodes the system's covariance, using the transfer function's unique recovery and symplectic transformations.

Contribution

It establishes the conditions under which system parameters can be identified from the power spectrum and provides a method to construct system realizations from it.

Findings

Transfer function can be uniquely recovered from the power spectrum.

Equivalent systems are related by symplectic transformations.

Parameters identifiable from the power spectrum depend on the transfer function.

Abstract

In this paper we investigate system identification for general quantum linear systems. We consider the situation where the input field is prepared as stationary (squeezed) quantum noise. In this regime the output field is characterised by the power spectrum, which encodes covariance of the output state. We address the following two questions: (1) Which parameters can be identified from the power spectrum? (2) How to construct a system realisation from the power spectrum? The power spectrum depends on the system parameters via the transfer function. We show that the transfer function can be uniquely recovered from the power spectrum, so that equivalent systems are related by a symplectic transformation.