The power of microscopic nonclassical states to amplify the precision of macroscopic optical metrology

TL;DR

This paper demonstrates that microscopic nonclassical states can significantly enhance macroscopic optical measurement precision, with optimal configurations identified through quantum Fisher information analysis, applicable to various metrology scenarios.

Contribution

It provides a comprehensive optimization of measurement configurations, revealing the quantum Fisher information as the key metric for maximum enhancement with nonclassical states.

Findings

Quantum Fisher information determines maximum metrological enhancement.

Mach-Zehnder interferometer is optimal for phase sensing with nonclassical states.

Extension to multi-mode states improves measurement precision.

Abstract

It is well-known that the precision of a phase measurement with a Mach-Zehnder interferometer employing strong (macroscopic) classic light can be greatly enhanced with the addition of a weak (microscopic) light field in a non-classical state. The resulting precision is much greater than that possible with either the macroscopic classical or microscopic quantum states alone. In the context of quantifying non-classicality, the amount by which a non-classical state can enhance precision in this way has been termed its "metrological power". Given the technological difficulty of producing high-amplitude non-classical states of light, this use of non-classical light is likely to provide a technological advantage much sooner than the Heisenberg scaling employing much stronger non-classical states. To date, the enhancement provided by weak nonclassical states has been calculated only for specific measurement configurations. Here we are able to optimize over all measurement configurations to obtain the maximum enhancement that can be achieved by any single or multi-mode nonclassical state together with strong classical states, for local and distributed quantum metrology employing any linear or nonlinear single-mode unitary transformation. Our analysis reveals that the quantum Fisher information for \textit{quadrature displacement sensing} is the sole property that determines the maximum achievable enhancement in all of these different scenarios, providing a unified quantification of the metrological power. It also reveals that the Mach-Zehnder interferometer is an optimal network for phase sensing for an arbitrary single-mode nonclassical input state, and how the Mach-Zehnder interferometer can be extended to make optimal use of any multi-mode nonclassical state for metrology.