Mihály Weiner (BME & Rényi): Hypothesis testing and a new characterization of matrix geometric means

Let $A, B, C$ be three positive semidefinite matrices. I will show that there exists a subexponential function (e.g. a polynomial) $p$ such that $A^{\otimes n}  \leq p(n) (B^{\otimes n} + C^{\otimes n})$ for all $n = 1,2,3,\dots$ if and only if there exists a $t \in [0,1]$ such that  $A \leq B \#_{t} C$
where $B \#_{t} C$ is the weighted geometric mean of $B$ and $C$. I will also explain why this question appears in asymptotic quantum hypothesis testing. Joint work with P.E. Frenkel, M. Mosonyi and P. Vrana.