Mutual information--based approach to adaptive homodyne detection of quantum optical states

I propose an approach to adaptive homodyne detection of digitally modulated quantum optical pulses in which the phase of the local oscillator is chosen to maximize the average information gain, i.e., the mutual information, at each step of the measurement. I study the properties of this adaptive detection scheme by considering the problem of classical information content of ensembles of coherent states. Using simulations of quantum trajectories and visualizations of corresponding measurement operators, I show that the proposed measurement scheme adapts itself to the features of each ensemble. For all considered ensembles of coherent states, it consistently outperforms heterodyne detection and Wiseman's adaptive scheme for phase measurements [H.M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)].