Identification of single-input-single-output quantum linear systems

TL;DR

This paper investigates the identification of parameters in single-input-single-output quantum linear systems, focusing on how output measurements relate to system parameters and how to reconstruct system models from data.

Contribution

It characterizes the identifiability of quantum linear systems using input-output data, including the role of symplectic transformations and power spectra in system realization.

Findings

Identifiable parameters depend on input type and system symmetries.

Power spectrum fully determines the transfer function in cascade systems.

A method for constructing globally minimal systems from the power spectrum is provided.

Abstract

The purpose of this paper is to investigate system identification for single-input-single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be identified by measuring the output? (2) How can we construct a system realization from sufficient input-output data? We show that for time-dependent inputs, the systems which cannot be distinguished are related by symplectic transformations acting on the space of system modes. This complements a previous result for passive linear systems. In the regime of stationary quantum noise input, the output is completely determined by the power spectrum. We define the notion of global minimality for a given power spectrum, and characterize globally minimal systems as those with a fully mixed stationary state. We show that in the case of systems with a cascade realization, the power spectrum completely fixes the transfer function, so the system can be identified up to a symplectic transformation. We give a method for constructing a globally minimal subsystem direct from the power spectrum. Restricting to passive systems the analysis simplifies so that identifiability may be completely understood from the eigenvalues of a particular system matrix.