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Equivalence classes and local asymptotic normality in system identification for quantum Markov chains

Guţă, Mădălin; Kiukas, Jukka

Authors

Jukka Kiukas



Abstract

We consider the problem of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. The starting point of the analysis is the fact that the knowledge of the output state completely fixes the dynamics up to an equivalence class of ‘coordinate transformation’ consisting of a multiplication by a phase and a unitary conjugation of the Kraus operators.

Assuming that the dynamics depends on an unknown parameter, we show that the latter can be estimated at the ‘standard’ rate n−1/2, and give an explicit expression of the (asymptotic) quantum Fisher information of the output, which is proportional to the Markov variance of a certain ‘generator’. More generally, we show that the output is locally asymptotically normal, i.e., it can be approximated by a simple quantum Gaussian model consisting of a coherent state whose mean is related to the unknown parameter. As a consistency check, we prove that a parameter related to the ‘coordinate transformation’ unitaries has zero quantum Fisher information.

Journal Article Type Article
Publication Date May 31, 2015
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 335
Issue 3
APA6 Citation Guţă, M., & Kiukas, J. (2015). Equivalence classes and local asymptotic normality in system identification for quantum Markov chains. Communications in Mathematical Physics, 335(3), doi:10.1007/s00220-014-2253-0
DOI https://doi.org/10.1007/s00220-014-2253-0
Publisher URL https://doi.org/10.1007/s00220-014-2253-0
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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