Photon statistics without photon counting S. Olivares, A. R. Rossi, M. G. A. Paris, G. Zambra...
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Transcript of Photon statistics without photon counting S. Olivares, A. R. Rossi, M. G. A. Paris, G. Zambra...
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)
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)
SummarySummary
•Why the photon distribution ? Why not photon counting ?
•MaxLik estimation: iterative solution
•Experimental verification
•Outlooks
•Why the photon distribution ? Why not photon counting ?
•MaxLik estimation: iterative solution
•Experimental verification
•Outlooks
Photon distributionPhoton distribution
•Nonclassicality
•Channel capacity
•Quantum radiography
•Nonclassicality
•Channel capacity
•Quantum radiography
Photon countingPhoton counting
• Photomultipliers / Hybrid photodetectors
• Solid state detectors
• Thermal detectors
• Homodyne detection (Quantum Tomography)
• Photomultipliers / Hybrid photodetectors
• Solid state detectors
• Thermal detectors
• Homodyne detection (Quantum Tomography)
On/Off detectionOn/Off detection
Multiple quantum efficienciesMultiple quantum efficiencies}}
LINPOS problemLINPOS problem
On/Off statisticsOn/Off
statistics
ηη quantum efficiencyquantum efficiency
•Probability distribution
•Random sample
• Joint probability of the sample
•Probability distribution
•Random sample
• Joint probability of the sample
MaxLik estimationMaxLik estimation
Maxlik estimation ➞ take the value of the parameters which maximize the likelihood of the observed data
Maxlik estimation ➞ take the value of the parameters which maximize the likelihood of the observed data
➥➥
Likelihood of the data setLikelihood of the data set
Maximization of a function of several variables (numerical, time-consuming)Maximization of a function of several variables (numerical, time-consuming)
MaxLik Estimation of MaxLik Estimation of
Iterative solution Iterative solution
•Convergence
•Accuracy
•Robustness
•Convergence
•Accuracy
•Robustness
Iterative solution Iterative solution
Convergence Convergence
# iterations x 1000# iterations x 1000
Iterative solution Iterative solution
AccuracyAccuracy
Robustness to fluctuations on ηRobustness to fluctuations on η
QuickTime™ and aVideo decompressor
are needed to see this picture.
Coherent stateCoherent state
CW regimeCW regime
Weak coherent stateWeak coherent state
“Heralded” single-photon state“Heralded” single-photon state
Pulsed regimePulsed regime
GaussianGaussian
ThermalThermal
MultithermalMultithermal
Current developmentsCurrent developments
•Extension to two or more modes (IEN)
•Comparison with schemes involving one-photon-resolving detectors
• Improving the approximation (Z. Hradil & J. Rehacek, Olomouc, Czech Rep)
•Extension to two or more modes (IEN)
•Comparison with schemes involving one-photon-resolving detectors
• Improving the approximation (Z. Hradil & J. Rehacek, Olomouc, Czech Rep)
•Reconstruction of the whole density matrix
•Reconstruction of the Wigner function (Insubria)
•Reconstruction of the whole density matrix
•Reconstruction of the Wigner function (Insubria)
OutlooksOutlooks
ReferencesReferences
qinf.fisica.unimi.it/~paris/qinf.fisica.unimi.it/~paris/