Photon statistics without photon counting S Olivares A

Photon statistics without photon counting S. Olivares, A. R. Rossi, M. G. A. Paris , G. Zambra (Uni. Mi) A. Andreoni, M. Bondani (Uni. Insubria) M. Genovese, M. Gramegna, G. Brida (IEN-To)

Summary • Why the photon distribution ? Why not photon counting ? • Max. Lik 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

Max. Lik 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 Max. Lik 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

CW regime Weak coherent state “Heralded” single-photon state

Pulsed regime Gaussian Thermal Multithermal

Current developments • Extension to two or more modes • Comparison with schemes involving photon-resolving detectors • Improving the approximation Hradil & J. Rehacek, Olomouc, Czech Rep) (IEN) one(Z.

Outlooks • Reconstruction of the whole density matrix • Reconstruction of the Wigner function (Insubria) References qinf. fisica. unimi. it/~paris/