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.

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