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From quasientropy to various quantum information quantities
 PUBL. RIMS KYOTO UNIV. 48(2012), 525–542.
, 2012
"... The subject is the applications of the use of quasientropy in finite dimensional spaces to many important quantities in quantum information. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the fdivergence, monotone metrics, covariance an ..."
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The subject is the applications of the use of quasientropy in finite dimensional spaces to many important quantities in quantum information. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the fdivergence, monotone metrics, covariance and the χ 2divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone metrics are also characterized by their joint convexity property.
Concavity of certain matrix trace and norm functions. Linear Algebra and its
 Applications
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Remarks on Kim’s strong subadditivity matrix inequality: extensions and equality conditions
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unknown title
, 2009
"... On the quantum frelative entropy and generalized data processing inequalities ..."
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On the quantum frelative entropy and generalized data processing inequalities
unknown title
, 2009
"... On the quantum frelative entropy and generalized data processing inequalities ..."
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On the quantum frelative entropy and generalized data processing inequalities
Convexity of quasientropy type functions: Lieb’s and Ando’s convexity theorems revisited
 J. MATH. PHYS. 54, 062201 (2013)
, 2013
"... Given a positive function f on (0, ∞) and a nonzero real parameter θ, we consider a function I θ f (A, B, X) = Tr X ∗ (f(LAR −1 B)RB) −θ (X) in three matrices A, B> 0 and X. This generalizes the notion of monotone metrics on positive definite matrices, and in the literature θ = ±1 has been typi ..."
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Given a positive function f on (0, ∞) and a nonzero real parameter θ, we consider a function I θ f (A, B, X) = Tr X ∗ (f(LAR −1 B)RB) −θ (X) in three matrices A, B> 0 and X. This generalizes the notion of monotone metrics on positive definite matrices, and in the literature θ = ±1 has been typical. We investigate how operator monotony of f is sufficient and/or necessary for joint convexity/concavity of Iθ f (A, B, X). Similar discussions are given for quasientropies and quantum skew informations.
From quasientropy
"... The subject is the overview of the use of quasientropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the fdivergence, monotone metrics, covariance and the χ2divergence are the most important particular ca ..."
Abstract
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The subject is the overview of the use of quasientropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the fdivergence, monotone metrics, covariance and the χ2divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone metrics are also characterized by their joint convexity property.