F. Hiai

activity

20052026

most citedQuantum f-divergences and error correction

174 citations · 243 across the 17 of their papers we have counts for

collaborators

Showing math.FAShow all

5 papers · 1 filter

math.FA2025

Log-majorizations between quasi-geometric type means for matrices

Fumio Hiai

In this paper, for $α \in (0, \infty) ∖ {1}$ , $p > 0$ and positive semidefinite matrices $A$ and $B$ , we consider the quasi-extension $\mathcal{M}_{α,p}(A,B):=\mathcal{M}_α(A^p,…

math.FA2025

Various inequalities between quasi-arithmetic mean and quasi-geometric type means for matrices

Fumio Hiai

In this paper, for $0 < α < 1$ , $p > 0$ and positive semidefinite matrices $A, B \geq 0$ , we consider the quasi-extension $A_{α, p} (A, B) := ((1 - α) A^{p} + α B^{p})^{1/ p}$ of the $α$ -weighted…

math.FA2024

Log-majorization and matrix norm inequalities with application to quantum information

Fumio Hiai

We are concerned with log-majorization for matrices in connection with the multivariate Golden--Thompson trace inequality and the Karcher mean (i.e., a multivariate extension of th…

math.FA2014★ 1 cited

Anti Lie-Trotter formula

K. M. R. Audenaert, F. Hiai

Let $A$ and $B$ be positive semidefinite matrices. The limit of the expression $Z_{p} := (A^{p /2} B^{p} A^{p /2})^{1/ p}$ as $p$ tends to $0$ is given by the well known Lie-Trotter-Kato form…

math.FA2010

Strongly subadditive functions

Koenraad Audenaer, Fumio Hiai, Denes Petz

Let f be a function defined on positive numbers. The subject is the trace inequality $Tr f(A) + Tr f(P_2AP_2) \le Tr f(P_{12}AP_{12}) + \Tr f(P_{23}AP_{23})$, where $A$ is a positi…