A formulation of Rényi entropy on \(C^*\)-algebras

  • Farrukh Mukhamedov
  • Kyouhei OhmuraEmail author
  • Noboru Watanabe


The entropy of probability distribution defined by Shannon has several extensions. Renyi entropy is one of the general extensions of Shannon entropy and is widely used in engineering, physics, and so on. On the other hand, the quantum analogue of Shannon entropy is von Neumann entropy. Furthermore, the formulation of this entropy was extended to on \(C^*\)-algebras by Ohya (\(\mathcal {S}\)-mixing entropy). In this paper, we formulate Renyi entropy on \(C^*\)-algebras based on \(\mathcal {S}\)-mixing entropy and prove several inequalities for the uncertainties of states in various reference systems.


Quantum information theory Quantum entropy \(\mathcal {S}\)-mixing entropy Rényi entropy Quantum statistical mechanics Operator algebras 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, College of ScienceUnited Arab Emirates UniversityAl-AinUnited Arab Emirates
  2. 2.Department of Information SciencesTokyo University of ScienceNoda CityJapan

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