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

¹ Qatar Center for Quantum Computing, College of Science and Engineering, Hamad Bin Khalifa University - Doha, Qatar
² Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan - Kelowna, BC V1V 1V7, Canada
³ Department of Physics, National Institute of Technology Srinagar - Srinagar, Jammu and Kashmir 190006, India
⁴ Canadian Quantum Research Center - 204-3002, 32 Ave Vernon, BC V1T 2L7 Canada
⁵ Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan - Kelowna, BC V1V 1V7, Canada
⁶ Department of Quantum Science and Technology, Research School of Physics, The Australian National University - Canberra, ACT 2601, Australia

Received: 10 July 2023
Accepted: 11 December 2023

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 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.