Classifying deviation from standard quantum behavior using the Kullback-Leibler divergence

In this letter, we propose a novel statistical method to measure which system is better suited to probe small deviations from the usual quantum behavior. Such deviations are motivated by a number of theoretical and phenomenological motivations, and various systems have been proposed to test them. We propose that measuring deviations from quantum mechanics for a system would be easier if it had a higher Kullback-Leibler divergence. We show this explicitly for a non-local Scrödinger equation and argue that it will hold for any modification to standard quantum behavior. Thus, the results of this letter can be used to classify a wide range of theoretical and phenomenological models.