Nonlocality under uncertainty-disturbance relations and self-duality

We exploit the interplay between uncertainty, disturbance, nonlocality, and self-duality within the framework of generalized probabilistic theories (GPTs). We first introduce an operational uncertainty-disturbance relation that reveals the discrepancies of GPTs in uncertainty and disturbance exhibited by one single measurement. We then apply the relation to Bell's scenarios and derive upper bounds for the basic spatial Clauser-Horne-Shimony-Holt and the temporal Leggett-Garg inequalities with and without the assumption of strong self-duality, respectively. It turns out that self-duality, though being thought of as one pillar of the axiomatization of quantum theory and implying additional constraints, is insufficient to explain the quantum violations. These insights may serve as a seed for a universal understanding of these basic properties in GPTs.

Automated summary

In this study, we explore the interplay between uncertainty, disturbance, nonlocality, and self-duality within the framework of generalized probabilistic theories (GPTs). By introducing an operational uncertainty-disturbance relation, we reveal the discrepancies in uncertainty and disturbance exhibited by GPTs in a single measurement. This relation is then applied to Bell's scenarios, resulting in upper bounds for the basic Clauser-Horne-Shimony-Holt and Leggett-Garg inequalities. Our findings show that self-duality, despite being considered a pillar of quantum theory, is insufficient to explain quantum violations. These insights may contribute to a universal understanding of these fundamental properties in GPTs.