Matrix trace inequalities related to the Tsallis relative entropies of real order
In this paper, we show matrix trace inequalities related to the Tsallis relative entropy of real order: For positive definite matrices ρ and σ, and each 0<α≤1Dα(ρ|σ)≤−Tr[ρ1−qqTαq(ρq|σq)] for all q≥α>0, where the Tsallis relative entropy Dα(ρ|σ) is defined by Dα(ρ|σ)=−Tr(ρ1−ασα−ρα) and the Tsal...
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Published in | Journal of mathematical analysis and applications Vol. 498; no. 1; p. 124877 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.06.2021
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Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we show matrix trace inequalities related to the Tsallis relative entropy of real order: For positive definite matrices ρ and σ, and each 0<α≤1Dα(ρ|σ)≤−Tr[ρ1−qqTαq(ρq|σq)] for all q≥α>0, where the Tsallis relative entropy Dα(ρ|σ) is defined by Dα(ρ|σ)=−Tr(ρ1−ασα−ρα) and the Tsallis relative operator entropy Tα(ρ|σ) is defined by Tα(ρ|σ)=ρ♯ασ−ρα, where ♯α is the matrix α-geometric mean. Moreover, we show estimates of the difference between two Tsallis relative entropies of real order. |
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ISSN: | 0022-247X 1096-0813 |
DOI: | 10.1016/j.jmaa.2020.124877 |