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Quantum Entropy Information Measures

Relative operator entropies and Tsallis relative operator entropies in JB-algebras

arXiv
Authors: Shuzhou Wang, Zhenhua Wang

Year

2020

Paper ID

533

Status

Preprint

Abstract Read

~2 min

Abstract Words

101

Citations

N/A

Abstract

We initiate the study of relative operator entropies and Tsallis relative operator entropies in the setting of JB-algebras. We establish their basic properties and extend the operator inequalities on relative operator entropies and Tsallis relative operator entropies to this setting. In addition, we improve the lower and upper bounds of the relative operator (α, β)-entropy in the setting of JB-algebras that were established in Hilbert space operators setting by Nikoufar [18, 20]. Though we employ the same notation as in the classical setting of Hilbert space operators, the inequalities in the setting of JB-algebras have different connotations and their proofs requires techniques in JB-algebras.

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  • This paper contributes to the Quantum Entropy & Information Measures research area in the Quantum Articles archive.
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  • We initiate the study of relative operator entropies and Tsallis relative operator entropies in the setting of JB-algebras.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2012.13480 [2] arXiv https://arxiv.org/abs/2012.13480 [3] Publisher https://arxiv.org/abs/2012.13480

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