4.6 Article

Entropic uncertainty relations in a class of generalized probabilistic theories

Journal

Publisher

IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac0c5c

Keywords

generalized probabilistic theories; uncertainty relations; measurement incompatibility; foundation of quantum physics

Funding

  1. JSPS KAKENHI [JP20K03732, JP21J10096]

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The study explores entropic uncertainty relations in generalized probabilistic theories and proves that these relations can be obtained in these theories, showing that the entropic structure in uncertainty relations is not limited to quantum theory.
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 (2014 Phys. Rev. Lett. 112 050401) are proved in those theories. These results manifest that the entropic structure in the uncertainty relations is not restricted to quantum theory and therefore is universal one. Concrete calculations of our relations in GPTs called the regular polygon theories are also demonstrated.

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