Fisher information and asymptotic normality in system identification for quantum Markov chains

Journal Article · Wed Jun 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.062324· OSTI ID:21550074

Guta, Madalin ^[1]

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1. University of Nottingham, School of Mathematical Sciences, University Park, Nottingham NG7 2RD (United Kingdom)

This paper deals with the problem of estimating the coupling constant {theta} of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of {theta} whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.

• OSTI ID: 21550074
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
COUPLING CONSTANTS
ERRORS
FUNCTIONS
GAUSS FUNCTION
INFORMATION
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
SCALING
STOCHASTIC PROCESSES