Experimental phase estimation enhanced by machine learning

Quantum metrology represents one of the most promising applications of quantum theory. Its main objective is to measure a set of unknown physical parameters by exploiting quantum resources to obtain enhanced precision with... [ view full abstract ]

Quantum metrology represents one of the most promising applications of quantum theory. Its main objective is to measure a set of unknown physical parameters by exploiting quantum resources to obtain enhanced precision with respect to the classical case. Phase estimation provides a notable benchmark to develop and test experimentally suitable methodologies to be applied in the general scenario. In this case, the parameter to be estimated is an optical phase embedded in an interferometer. The general approach employs sending input probe states and measuring the output to retrieve information on the unknown parameters. In the last few years, experimental and theoretical efforts have been devoted to define the precision bounds and how to reach them. These analyses define the framework to reach ultimate precision in the asymptotic limit of a large number of measurement. However, in several applications it is crucial to obtain the capability of reaching optimal performances by using only a limited number of resources. It is thus necessary to develop adaptive methodologies for this purpose. Machine learning, the capability of a computer to make data-driven decisions, represents a promising tool in this direction.

We will discuss the application of machine learning methods to implement adaptive phase estimation protocols able to reach optimal precision by employing a limited number of measurements. More specifically, we will report the single-photon experimental implementation of a novel Bayesian adaptive protocol [1] which is capable of reaching optimal precision with a small number of trials. We will compare the performances of such approach with respect to other non-adaptive and adaptive strategies, showing its capability to optimize the extraction of information from the unknown phase. Furthermore, we show that such protocol presents a significant resilience to experimental noise, thus rendering it suitable for its application in realistic conditions.
We will finally discuss perspectives to the multiparameter scenario. In this case, the theoretical framework still presents open problems, and adaptive protocols are necessary in several instances to optimize the simultaneous extraction of information for all parameters.

Reference

[1] A. Lumino, E. Polino, A. S. Rab, G. Milani, N. Spagnolo, N. Wiebe, F. Sciarrino, arXiv:1712.07570 (2017).