1. A method for extracting information from a Josephson comparator, the method comprising: obtaining a set of predetermined probabilities of observing an output pulse from a Josephson comparator, each probability corresponding to a valid set of discrete parameter values of an input signal to the Josephson comparator; collecting a set of outputs produced by the Josephson comparator in response to sampling the input signal; computing one or more threshold values for counts of output pulses from the Josephson comparator with respect to the size of the set of outputs; determining an empirical count of output pulses; and hypothesizing the discrete parameter values of the input signal by comparing the empirical count of output pulses against the one or more threshold values; wherein: at least a subset of outputs in the set of outputs are produced by a set of one or more input signal parameter values that lie within a gray zone of the Josephson comparator.