Efficient Bayesian phase estimation via entropy-based sampling

Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable auxiliary phase. Here, we present a Bayesian phase estimation (BPE) algorithm with an ingenious update rule of the auxiliary phase designed via entropy-based sampling. Unlike other adaptive BPE algorithms, the auxiliary phase in our algorithm is determined only once in a pre-estimation step. With simple statistical analysis on a small batch of data, an iteration rule for the auxiliary phase is pre-established and used in all afterward updates, instead of complex calculations in every update trails. During this pre-estimation process the most informative data can be selected, which guides one to perform the BPE with much less measurement times. As the measurement times for the same amount of Bayesian updates is significantly reduced, our algorithm via entropy-based sampling can work as efficient as other adaptive BPE algorithms and shares the advantages (such as wide dynamic range and perfect noise robustness) of non-adaptive BPE algorithms. Our algorithm is of promising applications in various practical quantum sensors such as atomic clocks and quantum magnetometers.

Automated summary

This paper presents a Bayesian phase estimation algorithm with an ingenious update rule of the auxiliary phase using entropy-based sampling. Unlike other adaptive algorithms, the auxiliary phase in this algorithm is determined only once in a pre-estimation step. By selecting informative data, the algorithm reduces the number of measurements required. The algorithm has promising applications in various practical quantum sensors.