Entropic Uncertainty Relations in a Class of Generalized Probabilistic Theories

TL;DR

This paper investigates entropic uncertainty relations within a broad class of generalized probabilistic theories, extending quantum uncertainty concepts and demonstrating their universal applicability beyond quantum mechanics.

Contribution

It introduces methods to derive entropic uncertainty relations in GPTs and shows their similarity to quantum relations, highlighting the universality of entropic structures.

Findings

Derived entropic preparation uncertainty relations in GPTs

Established entropic measurement uncertainty relations in GPTs

Applied relations to regular polygon theories

Abstract

Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized probabilistic theories (GPTs). The current study explores two types of entropic uncertainty relations, preparation and measurement uncertainty relations, in a class of GPTs which can be considered generalizations of quantum theory. Not only a method for obtaining entropic preparation uncertainty relations but also an entropic measurement uncertainty relation similar to the quantum one by Buscemi et al. [Phys. Rev. Lett., 112, 050401] are proved in those theories. It manifests that the entropic structure of uncertainty relations in quantum theory is more universal. Concrete calculations of our relations in GPTs called the regular polygon theories are also demonstrated.