Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics
This paper deals with the problem of identifying and estimating dynamical parameters of continuous-time Markovian quantum open systems, in the input-output formalism. First, we characterise the space of identifiable parameters for ergodic dynamics, assuming full access to the output state for arbitr...
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| Format: | Article |
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American Institute of Physics
2017
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| Online Access: | https://eprints.nottingham.ac.uk/42291/ |
| _version_ | 1848796455265894400 |
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| author | Guţă, Mădălin Kiukas, Jukka |
| author_facet | Guţă, Mădălin Kiukas, Jukka |
| author_sort | Guţă, Mădălin |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This paper deals with the problem of identifying and estimating dynamical parameters of continuous-time Markovian quantum open systems, in the input-output formalism. First, we characterise the space of identifiable parameters for ergodic dynamics, assuming full access to the output state for arbitrarily long times, and show that the equivalence classes of undistinguishable parameters are orbits of a Lie group acting on the space of dynamical parameters. Second, we define an information geometric structure on this space, including a principal bundle given by the action of the group, as well as a compatible connection, and a Riemannian metric based on the quantum Fisher information of the output. We compute the metric explicitly in terms of the Markov covariance of certain "fluctuation operators", and relate it to the horizontal bundle of the connection. Third, we show that the system-output and reduced output state satisfy local asymptotic normality, i.e. they can be approximated by a Gaussian model consisting of coherent states of a multimode continuos variables system constructed from the Markov covariance “data". We illustrate the result by working out the details of the information geometry of a physically relevant two-level system. |
| first_indexed | 2025-11-14T19:48:15Z |
| format | Article |
| id | nottingham-42291 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:48:15Z |
| publishDate | 2017 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-422912020-05-04T18:45:54Z https://eprints.nottingham.ac.uk/42291/ Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics Guţă, Mădălin Kiukas, Jukka This paper deals with the problem of identifying and estimating dynamical parameters of continuous-time Markovian quantum open systems, in the input-output formalism. First, we characterise the space of identifiable parameters for ergodic dynamics, assuming full access to the output state for arbitrarily long times, and show that the equivalence classes of undistinguishable parameters are orbits of a Lie group acting on the space of dynamical parameters. Second, we define an information geometric structure on this space, including a principal bundle given by the action of the group, as well as a compatible connection, and a Riemannian metric based on the quantum Fisher information of the output. We compute the metric explicitly in terms of the Markov covariance of certain "fluctuation operators", and relate it to the horizontal bundle of the connection. Third, we show that the system-output and reduced output state satisfy local asymptotic normality, i.e. they can be approximated by a Gaussian model consisting of coherent states of a multimode continuos variables system constructed from the Markov covariance “data". We illustrate the result by working out the details of the information geometry of a physically relevant two-level system. American Institute of Physics 2017-05-15 Article PeerReviewed Guţă, Mădălin and Kiukas, Jukka (2017) Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics. Journal of Mathematical Physics, 58 . 052201. ISSN 1089-7658 http://aip.scitation.org/doi/10.1063/1.4982958 doi:10.1063/1.4982958 doi:10.1063/1.4982958 |
| spellingShingle | Guţă, Mădălin Kiukas, Jukka Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics |
| title | Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics |
| title_full | Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics |
| title_fullStr | Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics |
| title_full_unstemmed | Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics |
| title_short | Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics |
| title_sort | information geometry and local asymptotic normality for multi-parameter estimation of quantum markov dynamics |
| url | https://eprints.nottingham.ac.uk/42291/ https://eprints.nottingham.ac.uk/42291/ https://eprints.nottingham.ac.uk/42291/ |