Entropic Uncertainty Relations in a Class of Generalized Probabilistic 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.

18 pages, 3 tables

References in corpus (7)

• Heisenberg's Uncertainty Principle
• Higher-order interference and single-system postulates characterizing quantum theory
• Rényi entropy uncertainty relation for successive projective measurements
• All measurements in a probabilistic theory are compatible if and only if the state space is a simplex
• Generalized Landau-Pollak Uncertainty Relation
• Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements

Cited by in corpus (4)

• General probabilistic theories: An introduction
• Simulating all multipartite non-signalling channels via quasiprobabilistic mixtures of local channels in generalised probabilistic theories
• An uncertainty relation for measurements of random unitary channels acting on a qubit
• Comparing quantum incompatibility of device sets from an operational perspective