# Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit. (arXiv:1802.01452v1 [quant-ph])

Bounds on the ultimate precision attainable in the estimation of a parameter

in Gaussian quantum metrology are obtained when the average number of bosonic

probes is fixed. We identify the optimal input probe state among generic (mixed

in general) Gaussian states with a fixed average number of probe photons for

the estimation of a parameter contained in a generic multimode interferometric

optical circuit, namely, a passive linear circuit preserving the total number

of photons. The optimal Gaussian input state is essentially a single-mode

squeezed vacuum, and the ultimate precision is achieved by a homodyne

measurement on the single mode. We also reveal the best strategy for the

estimation when we are given $L$ identical target circuits and are allowed to

apply passive linear controls in between with an arbitrary number of ancilla

modes introduced.