Adaptive characterization of coherent states

Markku P. V. Stenberg, Kevin Pack, Frank K. Wilhelm

Published 2015-08-18Version 1

We present methods for efficient characterization of an optical coherent state $|\alpha\rangle$. We choose measurement settings adaptively and stochastically, based on data while it is collected. Our algorithm divides the estimation in two distinct steps: (i) Before the first detection of vacuum state, the probability of choosing a measurement setting is proportional to detecting vacuum with the setting, which makes using too similar measurement settings twice unlikely and (ii) after the first detection of vacuum, we focus measurements in the region where vacuum is most likely to be detected. In step (i) [(ii)] the detection of vacuum (a photon) has a significantly larger effect on the shape of the posterior probability distribution of $\alpha$. Compared to nonadaptive schemes, our method makes the number of measurement shots required to achieve certain level of accuracy smaller approximately by a factor proportional to the area describing the initial uncertainty of $\alpha$ in phase space. While this algorithm is not directly robust against readout errors, we make it such by introducing repeated measurements in the step (i).