Heisenberg scaling precision in the estimation of functions of parameters

Abstract

We propose a metrological strategy reaching Heisenberg scaling precision in the estimation of functions of any number $l$ of arbitrary parameters encoded in a generic $M$-channel linear network. This scheme is experimentally feasible since it only employs a single-mode squeezed vacuum and homodyne detection on a single output channel. Two auxiliary linear network are required and their role is twofold: to refocus the signal into a single channel after the interaction with the interferometer, and to fix the function of the parameters to be estimated according to the linear network analysed. Although the refocusing requires some knowledge on the parameters, we show that the required precision on the prior measurement is shot-noise, and thus achievable with a classic measurement. We conclude by discussing two paradigmatic schemes in which the choice of the auxiliary stages allows to change the function of the unknown parameter to estimate.

10 pages, 3 figures

References in corpus (6)

• Quantum Optical Metrology -- The Lowdown on High-N00N States
• Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
• Optimal phase measurements with pure Gaussian states
• Phase estimation for thermal Gaussian states
• Bayesian estimation in homodyne interferometry
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• Minimum Entanglement Protocols for Function Estimation
• Non-adaptive Heisenberg-limited metrology with multi-channel homodyne measurements
• Optimal function estimation with photonic quantum sensor networks
• Heisenberg-scaling sensitivity in the estimation of two parameters in a Mach-Zehnder interferometer
• Heisenberg scaling based on population coding