6 problems

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 $A$ and $B$ be $n\times n$ density matrices with $\operatorname{supp}(A)\subset\operatorname{supp}(B)$. Let $\phi:M_n(\mathbb{C})\to M_k(\mathbb{C})$ be a completely positive t…

Let $\rho,\sigma\in M_n^{++}(\mathbb{C})$ be density matrices, let $\alpha>0$ with $\alpha\neq 1$, and define the sandwiched Rényi relative entropy by … For a completely positive u…

Completely contractive data-processing conjecture for trace-norm conditional mutual information. If

Completely contractive data-processing conjecture for conditional mutual information. For any channel $\mathcal{E}:C\rightarrow C'$ with trivial correctable algebra, there exists a…

No-improvement conjecture. The coherent-classical estimation cost satisfies