Equivalence Classes and Local Asymptotic Normality in System Identification for Quantum Markov Chains

Madalin Guta, Jukka Kiukas

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25 Citations (SciVal)

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
Original languageEnglish
Pages (from-to)1397–1428
Number of pages32
JournalCommunications in Mathematical Physics
Volume335
Issue number3
Early online date26 Nov 2014
DOIs
Publication statusPublished - 31 May 2015
Externally publishedYes

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