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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/