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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)

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Summary 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

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Photon distribution Nonclassicality Channel capacity Quantum radiography Nonclassicality Channel capacity Quantum radiography

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Photon 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)

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On/Off detection Multiple quantum efficiencies LINPOS problem On/Off statistics η η quantum efficiency

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Probability distribution Random sample Joint probability of the sample Probability distribution Random sample Joint probability of the sample MaxLik estimation Maxlik estimation take the value of the parameters which maximize the likelihood of the observed data

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Likelihood of the data set Maximization of a function of several variables (numerical, time-consuming) MaxLik Estimation of

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Iterative solution Convergence Accuracy Robustness Convergence Accuracy Robustness

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Iterative solution Convergence # iterations x 1000

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Iterative solution Accuracy Robustness to fluctuations on η Coherent state

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CW regime Weak coherent state Heralded single-photon state

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Pulsed regime Gaussian Thermal Multithermal

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Current 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)

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

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