Author

H. Osaka

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Preprint Oct 2026

Three-Point Trace Positivity:Schatten Norm Compression and Interpolating Metrics

Let $(\mathcal N,\nu)$ be a finite tracial von Neumann algebra and set $\mathcal{K}_r(P,Q)=\nu((P^{1/2}QP^{1/2})^r)$. We prove that $$ [\mathcal{K}_r(P_i,P_j)]_{i,j=1}^3\ge0, \qquad 1/2\le r\le1. $$ The range $1/2<r<1$ is new even for matrices, and order three is sharp for $1/2\le r<1$. This single mechanism resolves t...

T. Vuong, H. Osaka · 0 citations

Open access Jan 2025

Optimizing entanglement manipulation via algebraic–geometric decompositions and semi-definite programming hierarchies

An algebraic–geometric framework is developed that systematically simplifies optimization over separable channels—widely used as approximations of local operations—and strengthens the Doherty–Parrilo–Spedalieri (DPS) hierarchy for solving such problems.

Seiseki Akibue, Jisho Miyazaki, H. Osaka · Letters in Mathematical Phys... · 2 citations

Preprint Aug 2026

Alternative-mean trace divergences: geometry, data processing, and barycenters

Let $f:(0,\infty)\to(0,\infty)$ be a nontrivial normalized operator monotone function and set $s=f'(1)$. We introduce the alternative-mean trace functional $$ \altPhi_f(A,B) :=\Tr(A\nabla_s B) -\Tr\!\left( f(A^{-1}\sharp B)\,A\,f(A^{-1}\sharp B) \right). $$ on the positive definite cone. We prove that $\altPhi_f$ is a...

T. Vuong, H. Shudo, H. Osaka · 0 citations