A formulation of Rényi entropy on C∗ -algebras

Farrukh Mukhamedov; Kyouhei Ohmura; Noboru Watanabe

doi:10.1007/s11128-019-2430-3

A formulation of Rényi entropy on C^∗ -algebras

Farrukh Mukhamedov, Kyouhei Ohmura, Noboru Watanabe

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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 (S-mixing entropy). In this paper, we formulate Renyi entropy on C^∗-algebras based on S-mixing entropy and prove several inequalities for the uncertainties of states in various reference systems.

Original language	English
Article number	318
Journal	Quantum Information Processing
Volume	18
Issue number	10
DOIs	https://doi.org/10.1007/s11128-019-2430-3
Publication status	Published - Oct 1 2019

Keywords

Operator algebras
Quantum entropy
Quantum information theory
Quantum statistical mechanics
Rényi entropy
S-mixing entropy

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Statistical and Nonlinear Physics
Theoretical Computer Science
Signal Processing
Modelling and Simulation
Electrical and Electronic Engineering

Access to Document

10.1007/s11128-019-2430-3

Cite this

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title = "A formulation of R{\'e}nyi entropy on C∗ -algebras",

abstract = "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 (S-mixing entropy). In this paper, we formulate Renyi entropy on C∗-algebras based on S-mixing entropy and prove several inequalities for the uncertainties of states in various reference systems.",

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T1 - A formulation of Rényi entropy on C∗ -algebras

AU - Mukhamedov, Farrukh

AU - Ohmura, Kyouhei

AU - Watanabe, Noboru

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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 (S-mixing entropy). In this paper, we formulate Renyi entropy on C∗-algebras based on S-mixing entropy and prove several inequalities for the uncertainties of states in various reference systems.

AB - 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 (S-mixing entropy). In this paper, we formulate Renyi entropy on C∗-algebras based on S-mixing entropy and prove several inequalities for the uncertainties of states in various reference systems.

KW - Operator algebras

KW - Quantum entropy

KW - Quantum information theory

KW - Quantum statistical mechanics

KW - Rényi entropy

KW - S-mixing entropy

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