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

Matthew Levitt and Mădălin Guţă
Phys. Rev. A 95, 033825 – Published 22 March 2017

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 of Guţă and Yamamoto [IEEE Trans. Autom. Control 61, 921 (2016)] 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.

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  • Received 3 October 2016

DOI:https://doi.org/10.1103/PhysRevA.95.033825

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyInterdisciplinary PhysicsNetworksAtomic, Molecular & Optical

Authors & Affiliations

Matthew Levitt* and Mădălin Guţă

  • School of Mathematical Sciences, University of Nottingham, University Park, NG7 2RD Nottingham, United Kingdom

  • *pmxml2@nottingham.ac.uk

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Issue

Vol. 95, Iss. 3 — March 2017

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