Ultimate sensitivity of precision measurements with Gaussian quantum light : a multi-modal approach

TL;DR

This paper establishes the maximum achievable sensitivity in quantum parameter estimation using multimode Gaussian light and demonstrates that optimal measurement strategies involve homodyne detection of the most squeezed mode, without needing inter-mode correlations.

Contribution

It provides a general framework for the ultimate sensitivity limits in multimode Gaussian quantum metrology and shows that the best strategy is to focus on the most squeezed mode with homodyne detection.

Findings

Homodyne detection can reach the ultimate sensitivity limit.

Maximum sensitivity is achieved by using the most squeezed mode.

Quantum correlations between modes do not enhance sensitivity.

Abstract

Multimode Gaussian quantum light, which includes multimode squeezed and multipartite quadrature entangled light, is a very general and powerful quantum resource with promising applications in quantum information processing and metrology. In this paper, we determine the ultimate sensitivity in the estimation of any parameter when the information about this parameter is encoded in such light, irrespective of the information extraction protocol used in the estimation and of the measured observable. In addition we show that an appropriate homodyne detection scheme allows us to reach this ultimate sensitivity. We show that, for a given set of available quantum resources, the most economical way to maximize the sensitivity is to put the most squeezed state available in a well-de ned light mode. This implies that it is not possible to take advantage of the existence of squeezed fluctuations in other modes, nor of quantum correlations and entanglement between diff erent modes.