Transcript Photon statistics without photon counting

Photon statistics without
photon counting
S. Olivares, A. R. Rossi, M. G. A. Paris , G. Zambra (UniMi)
A. Andreoni, M. Bondani (UniInsubria)
M. Genovese, M. Gramegna, G. Brida (IEN-To)
Summary
• Why the photon distribution ?
Why not photon counting ?
• MaxLik estimation: iterative solution
• Experimental verification
• Outlooks
Photon distribution
• Nonclassicality
• Channel capacity
• Quantum radiography
Photon counting
• Photomultipliers / Hybrid photodetectors
•
Solid state detectors
•
Thermal detectors
•
Homodyne detection (Quantum Tomography)
On/Off detection
η quantum efficiency
Multiple quantum efficiencies
LINPOS problem
On/Off statistics
MaxLik estimation
• Probability distribution
• Random sample
• Joint probability of the sample
Maxlik estimation ➞ take the value of the parameters
which maximize the likelihood of the observed data
Likelihood of the data set
MaxLik Estimation of
➥
Maximization of a function of several
variables (numerical, time-consuming)
Iterative solution
• Convergence
• Accuracy
• Robustness
Iterative solution
Convergence
# iterations x 1000
Iterative solution
Accuracy
Robustness to fluctuations on η
Coherent state
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CW regime
Weak coherent state
“Heralded” single-photon state
Pulsed regime
Gaussian
Thermal
Multithermal
Current developments
• Extension to two or more modes
(IEN)
• Comparison with schemes involving
photon-resolving detectors
• Improving the approximation
(Z. Hradil & J. Rehacek, Olomouc, Czech Rep)
one-
Outlooks
• Reconstruction of the whole density matrix
• Reconstruction of the Wigner function (Insubria)
References
qinf.fisica.unimi.it/~paris/