2020/06/10 by Ryo Takakura, Takayuki Miyadera
Physics and Astronomy · #Class (philosophy) #Entropic uncertainty #Measurement uncertainty #Probabilistic logic #Quantum #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum probability #Relation (database) #Statistical Mechanics and Entropy #Uncertainty principle #quant-ph
paper · pdf · doi:10.1088/1751-8121/ac0c5c
18 pages, 3 tables
arxiv created 2020/06/10 · openalex created_date 2020/06/19 · openalex publication_date 2021/06/17 · arxiv updated 2021/08/11 · openalex updated_date 2026/08/05
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 (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.