Equivalence classes and local asymptotic normality in system identification for quantum Markov chains
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Published: |
Springer
2015
|
| Online Access: | https://eprints.nottingham.ac.uk/47091/ |
| _version_ | 1848797465496518656 |
|---|---|
| author | Guţă, Mădălin Kiukas, Jukka |
| author_facet | Guţă, Mădălin Kiukas, Jukka |
| author_sort | Guţă, Mădălin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:04:19Z |
| format | Article |
| id | nottingham-47091 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:04:19Z |
| publishDate | 2015 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-470912020-05-04T17:07:43Z https://eprints.nottingham.ac.uk/47091/ Equivalence classes and local asymptotic normality in system identification for quantum Markov chains Guţă, Mădălin Kiukas, Jukka 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. Springer 2015-05-31 Article PeerReviewed Guţă, Mădălin and Kiukas, Jukka (2015) Equivalence classes and local asymptotic normality in system identification for quantum Markov chains. Communications in Mathematical Physics, 335 (3). pp. 1397-1428. ISSN 1432-0916 https://doi.org/10.1007/s00220-014-2253-0 doi:10.1007/s00220-014-2253-0 doi:10.1007/s00220-014-2253-0 |
| spellingShingle | Guţă, Mădălin Kiukas, Jukka Equivalence classes and local asymptotic normality in system identification for quantum Markov chains |
| title | Equivalence classes and local asymptotic normality in system identification for quantum Markov chains |
| title_full | Equivalence classes and local asymptotic normality in system identification for quantum Markov chains |
| title_fullStr | Equivalence classes and local asymptotic normality in system identification for quantum Markov chains |
| title_full_unstemmed | Equivalence classes and local asymptotic normality in system identification for quantum Markov chains |
| title_short | Equivalence classes and local asymptotic normality in system identification for quantum Markov chains |
| title_sort | equivalence classes and local asymptotic normality in system identification for quantum markov chains |
| url | https://eprints.nottingham.ac.uk/47091/ https://eprints.nottingham.ac.uk/47091/ https://eprints.nottingham.ac.uk/47091/ |