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On asymptotic quantum statistical inference

Richard D. Gill and Mădălin I. Guţă

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Abstract

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

Source
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

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1362751183

Digital Object Identifier
doi:10.1214/12-IMSCOLL909

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

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

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

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. https://projecteuclid.org/euclid.imsc/1362751183.


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References

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