8 problems

Let $Q$ be a non-uniform distribution and $U$ the uniform distribution on a support of cardinality $2^n$. Let $T$ be the matrix with two rows, $Q$ and $U$, and $2^n$ columns. The q…

Seshadreesan et al.'s conjecture. The function $\widetilde{\Delta}_t(A,B,\phi)$ should be monotonically increasing in $t$. This monotonicity would imply the fidelity refinement of…

Let $P$ be a measure and let $\mathcal{C}$ be a class of measures. For each $0<\alpha<1$, let $\hat{Q}_{\alpha}$ be a reversed Rényi projection of $P$ on $\mathcal{C}$, when it exi…

Additivity conjecture. The above additivity holds for $\alpha\in[\frac{1}{2},1)$. If true, the regularized sandwiched Rényi mutual information in the strong converse exponent formu…

Consider experiments $P$ and $Q$ with finitely many states, and let Proposition 1 provide a set of necessary conditions for large-sample Blackwell dominance, expressed through the…

Let $s$ satisfy $-1/d<s\leq -1/(d+1)$, and let $Q$ be a generic probability measure that does not admit a first moment, so that … Consider the Rényi divergence projection of $Q$ on…

For a tripartite pure state $\rho_{ABC}$, define the conditional sandwiched Rényi entropy by … where $\sigma_B$ ranges over states on $B$, $I$ is the identity operator, and…

Generalized redundancy inequality. If $R_\alpha<\infty$, then there exists a unique redundancy achieving distribution $Q_{\mathrm{opt}}$, and, for every distribution $Q$,