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

Levitt, Matthew and Guţă, Mădălin (2017) Identification of single-input–single-output quantum linear systems. Physical Review A, 95 (3). 033825/1-033825/15. ISSN 2469-9934

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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.

Item Type: Article
Additional Information: Levitt, Matthew and Guţă, Mădălin "Identification of single-input–single-output quantum linear systems" Phys. Rev. A 95, 033825 – Published 22 March 2017
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1103/PhysRevA.95.033825
Depositing User: Eprints, Support
Date Deposited: 06 Mar 2017 11:41
Last Modified: 12 Oct 2017 14:41
URI: http://eprints.nottingham.ac.uk/id/eprint/41083

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