Agnostic Dolinar receiver for coherent-state classification

We consider the problem of discriminating quantum states, where the task is to distinguish two different quantum states with a complete classical knowledge about them, and the problem of classifying quantum states, where the task is to distinguish two classes of quantum states where no prior classical information is available but a finite number of physical copies of each class is given. In the case the quantum states are represented by coherent states of light, we identify intermediate scenarios where partial prior information is available. We evaluate an analytical expression for the minimum error when the quantum states are opposite and a prior on the amplitudes is known. Such a threshold is attained by complex positive operator-valued measurements that involve a highly nonlinear optical procedure. A suboptimal procedure that can be implemented with current technology is presented that is based on a modification of the conventional Dolinar receiver. We study and compare the performance of the scheme under different assumptions on the prior information available.