# Model selection for quantum homodyne tomography

ESAIM: Probability and Statistics (2009)

- Volume: 13, page 363-399
- ISSN: 1292-8100

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topKahn, Jonas. "Model selection for quantum homodyne tomography." ESAIM: Probability and Statistics 13 (2009): 363-399. <http://eudml.org/doc/250643>.

@article{Kahn2009,

abstract = {
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.
},

author = {Kahn, Jonas},

journal = {ESAIM: Probability and Statistics},

keywords = {Density matrix; model selection; pattern functions estimator;
penalized maximum likelihood estimator; penalized projection estimators;
quantum calibration; quantum tomography; wavelet estimator; Wigner function.; density matrix; penalized maximum likelihood estimator; quantum calibration; Wigner function},

language = {eng},

month = {9},

pages = {363-399},

publisher = {EDP Sciences},

title = {Model selection for quantum homodyne tomography},

url = {http://eudml.org/doc/250643},

volume = {13},

year = {2009},

}

TY - JOUR

AU - Kahn, Jonas

TI - Model selection for quantum homodyne tomography

JO - ESAIM: Probability and Statistics

DA - 2009/9//

PB - EDP Sciences

VL - 13

SP - 363

EP - 399

AB -
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.

LA - eng

KW - Density matrix; model selection; pattern functions estimator;
penalized maximum likelihood estimator; penalized projection estimators;
quantum calibration; quantum tomography; wavelet estimator; Wigner function.; density matrix; penalized maximum likelihood estimator; quantum calibration; Wigner function

UR - http://eudml.org/doc/250643

ER -

## References

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