1. Detector of “Schrödinger’s Cat” States of Light

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

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

4. Applications in Quantum Metrology

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

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

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

8. 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

9. 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”

10. 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

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