Detector of “Schrödinger’s Cat” States of Light

Detector of “Schrödinger’s Cat” States of Light Scheme of the detector Photon counting Non-classical Measurements Projective but Non-Ideal ! Squeezed Vacuum

Detector of “Schrödinger’s Cat” States of Light Retrodicted States and Quantum Properties : Idealized Case Projective but Non-Ideal !

Applications in Quantum Metrology

Applications in Quantum Metrology General scheme of the Predictive Estimation of a Parameter We must wait the results of measurements !

Applications in Quantum Metrology General scheme of the Retrodictive Estimation of a Parameter

Applications in Quantum Metrology Fisher Information and Cramér-Rao Bound Relative distance Fisher Information

Applications in Quantum Metrology Fisher Information and Cramér-Rao Bound Any estimation is limited by the Cramér-Rao bound Fisher Information is the variation rate of retrodictive probabilities under a variation of the parameter Number of repetitions

Applications in Quantum Metrology Retrodictive Estimation of a Parameter Projective but Non-Ideal ! Predictive Retrodictive The result “n” is uncertain even though we prepare its target state The target state is the most probable preparation leading to the result “n”

Applications in Quantum Metrology Illustration : Estimation of a phase-space displacement Optimal Minimum noise influence Fisher Information is optimal only when the measurement is projective and ideal

Applications in Quantum Metrology Predictive and Retrodictive Estimations of a phase-space displacement The Quantum Cramér-Rao Bound is reached …