Estimation with Heisenberg-Scaling Sensitivity of a Single Parameter Distributed in an Arbitrary Linear Optical Network

Abstract

Quantum sensing and quantum metrology propose schemes for the estimation of physical properties, such as lengths, time intervals, and temperatures, achieving enhanced levels of precision beyond the possibilities of classical strategies. However, such an enhanced sensitivity usually comes at a price: the use of probes in highly fragile states, the need to adaptively optimise the estimation schemes to the value of the unknown property we want to estimate, and the limited working range, are some examples of challenges which prevent quantum sensing protocols to be practical for applications. This work reviews two feasible estimation schemes which address these challenges, employing easily realisable resources, i.e., squeezed light, and achieve the desired quantum enhancement of the precision, namely the Heisenberg-scaling sensitivity. In more detail, it is here shown how to overcome, in the estimation of any parameter affecting in a distributed manner multiple components of an arbitrary M-channel linear optical network, the need to iteratively optimise the network. In particular, we show that this is possible with a single-step adaptation of the network based only on a prior knowledge of the parameter achievable through a “classical” shot-noise limited estimation strategy. Furthermore, homodyne measurements with only one detector allow us to achieve Heisenberg-limited estimation of the parameter. We further demonstrate that one can avoid the use of any auxiliary network at the price of simultaneously employing multiple detectors.

The Role of Auxiliary Stages in Gaussian Quantum Metrology

“…In recent years, much attention has been put in the study of metrological schemes that exploit quantum resources, such as entanglement and squeezing, to enhance the sensitivity in the estimation of physical properties beyond the possibilities of classical strategies, with applications to imaging [1,2], thermometry [3,4], mapping of magnetic fields [5,6] and gravitational waves detection [7], among others. One of the most emblematic quantum enhancements sought in quantum metrology is the renown Heisenberg limit , which consists in achieving a scaling of the estimation error in the number N of probes (typically photons, or atoms) of order of 1/N, which surpasses the classical (or shot-noise) limit 1/ √ N. Gaussian metrology, which specializes in the study of estimation schemes employing Gaussian states of light and squeezing as metrological resource [29][30][31][32], represents a promising path towards a feasible quantum-enhancement in estimation strategies and the Heisenberg-scaling sensitivity [33][34][35][36][37][38][39][40][41]. It exploits the possibility to reduce the intrinsic noise of the electromagnetic field quadratures below the quantum fluctuations of the vacuum.…”