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On asymptotic quantum statistical inference

Richard D. Gill and Mădălin I. Guţă

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We study asymptotically optimal statistical inference concerning the unknown state of $N$ identical quantum systems, using two complementary approaches: a “poor man’s approach” based on the van Trees inequality, and a rather more sophisticated approach using the recently developed quantum form of LeCam’s theory of Local Asymptotic Normality.

Chapter information

Banerjee, M., Bunea, F., Huang, J., Koltchinskii, V., and Maathuis, M. H., eds., From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013) , 105-127

First available in Project Euclid: 8 March 2013

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Primary: 62F12: Asymptotic properties of estimators
Secondary: 62P35: Applications to physics

quantum Cramér-Rao bound van Trees inequality local asymptotic normality quantum local asymptotic normality

Copyright © 2010, Institute of Mathematical Statistics


Gill, Richard D.; Guţă, Mădălin I. On asymptotic quantum statistical inference. From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, 105--127, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2013. doi:10.1214/12-IMSCOLL909.

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