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

Gu??, M?d?lin; Kiukas, Jukka

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.

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), https://doi.org/10.1007/s00220-014-2253-0

• Journal Article Type: Article
• Acceptance Date: Aug 28, 2014
• Online Publication Date: Nov 26, 2014
• Publication Date: May 31, 2015
• Deposit Date: Oct 9, 2017
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 335
• Issue: 3
• DOI: https://doi.org/10.1007/s00220-014-2253-0
• Public URL: https://nottingham-repository.worktribe.com/output/750910
• Publisher URL: https://doi.org/10.1007/s00220-014-2253-0
• Contract Date: Oct 9, 2017