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

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.
Keywords :
Type de document :
Pré-publication, Document de travail
2008
Domaine :

https://hal.archives-ouvertes.fr/hal-00311975
Contributeur : Katia Méziani <>
Soumis le : samedi 23 août 2008 - 12:39:04
Dernière modification le : mercredi 12 octobre 2016 - 01:01:26
Document(s) archivé(s) le : jeudi 3 juin 2010 - 18:46:49

### Fichiers

haltest.pdf
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### Identifiants

• HAL Id : hal-00311975, version 1
• ARXIV : 0808.3194

### Citation

Katia Méziani. Nonparametric goodness-of fit testing in quantum homodyne tomography with noisy data. 2008. <hal-00311975>

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