7 problems

Improvement conjecture. There might be a more clever way to use the state overlap for general Gaussian states to improve this inequality.

Let $A$ be a symmetric matrix of order $n$ whose diagonal entries are zero and whose off-diagonal entries belong to $\\{\pm 1\\}$. Let $J_n$ be the all-ones matrix and $I_n$ the id…

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

Let $\rho_{ABC}$ be a tripartite state with reduced states $\rho_{AB}$, $\rho_{BC}$, and $\rho_B$, and let $U,V,W$ be unitaries over $\mathcal{H}_{ABC}$. Let $I(A:C|B)_\rho$ denote…

Let $\rho_{ABC}$ be a tripartite state, with reduced states $\rho_{AB}$, $\rho_{BC}$, and $\rho_B$. Define … and … Here $I(A:C|B)_\rho$ denotes the quantum conditional mutual infor…

General trace commutator conjecture. There exists a constant $c$, independent of $d$, such that

Let $A$ and $B$ be positive definite matrices satisfying $\operatorname{Tr}(A+B)=1$. Trace commutator conjecture. There exists a constant $c$, independent of the dimensions of $A$…