Introduces r-deformed α-z-Rényi relative entropies that satisfy divergence axioms, obey data processing inequality in certain parameter ranges, and provide a tighter upper bound on Tsallis relative entropy for density operators than a prior bound.
On the Araki-Lieb-Thirring inequality
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abstract
We prove an inequality that complements the famous Araki-Lieb-Thirring (ALT) inequality for positive matrices $A$ and $B$, by giving a lower bound on the quantity $\trace[A^r B^r A^r]^q$ in terms of $\trace[ABA]^{rq}$ for $0\le r\le 1$ and $q\ge0$, whereas the ALT inequality gives an upper bound. The bound contains certain norms of $A$ and $B$ as additional ingredients and is therefore of a different nature than the Kantorovich type inequality obtained by Bourin (\textit{Math. Inequal. Appl.} \textbf{8}(2005) pp. 373--378) and others. Secondly, we also prove a generalisation of the ALT inequality to general matrices.
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2026 2verdicts
UNVERDICTED 2representative citing papers
A new texture measure T^GR_{α,z}(ρ) is defined from α-z Rényi relative entropy, relations among existing measures are analyzed, and texture witnesses are introduced with examples.
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$r$-deformed $\alpha$-$z$-R\'enyi relative entropy
Introduces r-deformed α-z-Rényi relative entropies that satisfy divergence axioms, obey data processing inequality in certain parameter ranges, and provide a tighter upper bound on Tsallis relative entropy for density operators than a prior bound.
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Quantifying and detecting quantum-state texture
A new texture measure T^GR_{α,z}(ρ) is defined from α-z Rényi relative entropy, relations among existing measures are analyzed, and texture witnesses are introduced with examples.