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

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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/