5 problems

Let $H_\alpha(\rho\|\sigma)$ and $D_\alpha(\rho\|\sigma)$ denote the paper's quantum Hellinger and Rényi divergences. Let $\overline H_\alpha(\rho\|\sigma)$ and…

Let $\rho$ and $\sigma$ be the states appearing in the definition of the quantum Hellinger divergence $H_\alpha(\rho\|\sigma)$, and let $\alpha>1$. Trace-representation conjecture.…

Let $M$ and $N$ be quantum measurements, and let $D$ denote the divergence used to define the entropic orderings $D_N\leq D_M$ and $S_N\geq S_M$. Write $D^{\max}$ for the maximal d…

Minimal Rényi interval conjecture. The dichotomies are interconvertible if and only if their minimal quantum Rényi divergences agree throughout the interval:

Minimal Rényi sufficiency conjecture. The family $D^{\alpha}_{\min}$ provides a sufficient family of divergences for interconversion of finite-dimensional density matrices via posi…