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

Levitt, Matthew; Guţă, Mădălin


Matthew Levitt


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.


Levitt, M., & Guţă, M. (in press). Identification of single-input–single-output quantum linear systems. Physical Review A, 95(3),

Journal Article Type Article
Acceptance Date Feb 27, 2017
Online Publication Date Mar 22, 2017
Deposit Date Mar 6, 2017
Publicly Available Date Mar 22, 2017
Journal Physical Review A
Print ISSN 2469-9926
Electronic ISSN 2469-9934
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 95
Issue 3
Article Number 033825
Public URL
Publisher URL
Copyright Statement Copyright information regarding this work can be found at the following address:
Additional Information Levitt, Matthew and Guta, Madalin "Identification of single-input–single-output quantum linear systems" Phys. Rev. A 95, 033825 – Published 22 March 2017


PhysRevA.95.033825.pdf (620 Kb)

Copyright Statement
Copyright information regarding this work can be found at the following address:

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