5 problems

Let $\omega$ be a quantum state, and let $\psi_1,\ldots,\psi_m$ be hypothesis states. In asymmetric multi-state discrimination, the given state is $\omega$ and the hypotheses are…

Let $\omega$ be a quantum state and let $\psi_1,\ldots,\psi_m$ be hypothesis states in an asymmetric multi-state discrimination problem. The multi-state Rényi divergences are the d…

Unamortized-divergence conjecture. The various channel divergences without amortization should characterize the asymptotic error exponents of interest, as they do in the classical…

Monotonicity conjecture. The $\alpha$-$z$ divergence is monotone with respect to $\alpha$ for fixed $z$.

Let $\N$ be the underlying von Neumann algebra, let $\N_*^+$ denote its positive normal linear functionals, and let $\N^+_{*1}$ denote the normalised positive functionals. For…