Quantum Metrology of Noisy Spreading Channels

We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy that attains the quantum Fisher information, whereas the customarily used homodyne detection becomes useless in the limit of small displacements, due to the same effect that gives Rayleigh's curse in optical superresolution. There is a quantum advantage: a squeezed or a Fock state with N average photons allow to asymptotically estimate the parameter with a V better precision than classical states with same energy. ffiffiffiN

Automated summary

This study provides an optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific parameter value. A physically relevant example of estimating displacement in the presence of phase randomizing noise is provided. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. Squeezed vacuum probe field is the optimal strategy for small displacement, while homodyne detection becomes useless in the limit of small displacements.