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

Levitt, Matthew; Guţă, Mădălin

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.

Citation

Levitt, M., & Guţă, M. (in press). Identification of single-input–single-output quantum linear systems. Physical Review A, 95(3), https://doi.org/10.1103/PhysRevA.95.033825

• 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
• DOI: https://doi.org/10.1103/PhysRevA.95.033825
• Public URL: http://eprints.nottingham.ac.uk/id/eprint/41083
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.033825
• Copyright Statement: Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
• 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