Model selection for quantum homodyne tomography
| dc.creator | Kahn, Jonas | |
| dc.date | 2007-12-18 | |
| dc.date.accessioned | 2026-07-07T08:49:52Z | |
| dc.date.available | 2026-07-07T08:49:52Z | |
| dc.description | This paper deals with a non-parametric problem coming from physics, namely quantum tomography. That consists in determining the quantum state of a mode of light through a homodyne measurement. We apply several model selection procedures: penalized projection estimators, where we may use pattern functions or wavelets, and penalized maximum likelihood estimators. In all these cases, we get oracle inequalities. In the former we also have a polynomial rate of convergence for the non-parametric problem. We finish the paper with applications of similar ideas to the calibration of a photocounter, a measurement apparatus counting the number of photons in a beam. Here the mathematical problem reduces similarly to a non-parametric missing data problem. We again get oracle inequalities, and better speed if the photocounter is good. | |
| dc.description | 40 pages, 2 figures, submitted to ESAIM: Probability and Statistics | |
| dc.identifier | https://arxiv.org/abs/0712.2912 | |
| dc.identifier | http://arxiv.org/abs/0712.2912 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144457 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G05, 81V80, 62P35 | |
| dc.title | Model selection for quantum homodyne tomography | |
| dc.type | text |