Classifying deviation from standard quantum behavior using Kullback Leibler divergence

TL;DR

This paper introduces a statistical approach using Kullback-Leibler divergence to identify which quantum systems are most effective for detecting small deviations from standard quantum mechanics, aiding in testing various models.

Contribution

It proposes a new method to classify systems based on their divergence from quantum behavior, applicable to a broad range of theoretical modifications.

Findings

Higher Kullback-Leibler divergence indicates better sensitivity to deviations

Explicit demonstration for a nonlocal Schrödinger equation

Applicable to various quantum deviation models

Abstract

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 has a higher Kullback Leibler divergence. We show this explicitly for a nonlocal Schrodinger equation and argue that it will hold for any modification to standard quantum behaviour. Thus, the results of this letter can be used to classify a wide range of theoretical and phenomenological models.