Electronic Journal of Statistics

Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data

Katia Meziani

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Abstract

In the framework of quantum optics, we study the problem of goodness-of-fit testing in a severely ill-posed inverse problem. A novel testing procedure is introduced and its rates of convergence are investigated under various smoothness assumptions. The procedure is derived from a projection-type estimator, where the projection is done in $\mathbb{L}_{2}$ distance on some suitably chosen pattern functions. The proposed methodology is illustrated with simulated data sets.

Article information

Source
Electron. J. Statist., Volume 2 (2008), 1195-1223.

Dates
First available in Project Euclid: 16 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1229450667

Digital Object Identifier
doi:10.1214/08-EJS286

Mathematical Reviews number (MathSciNet)
MR2461899

Zentralblatt MATH identifier
1320.62101

Subjects
Primary: 62G05: Estimation 62G10: Hypothesis testing 62G20: Asymptotic properties
Secondary: 81V80: Quantum optics

Keywords
Density matrix Goodness-of fit test Minimax rates Nonparametric test Pattern Functions estimation Quantum homodyne tomography Wigner function

Citation

Meziani, Katia. Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data. Electron. J. Statist. 2 (2008), 1195--1223. doi:10.1214/08-EJS286. https://projecteuclid.org/euclid.ejs/1229450667


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