5 problems

Generic compatibility conjecture. For generic $\boldsymbol{m}$ and $\boldsymbol{R}$, this equation can be solved with $\boldsymbol{A}\in E_r$, $\boldsymbol{B}\in E_s$, and…

Non-emptiness conjecture. The polytope $\mathcal{P}_{I,J,1}$ is non-empty if and only if, for every such $A$ and $B$, all four inequalities hold:

Compatibility conjecture. The displayed condition is equivalent to compatibility of the margins for all $r\times s\times2$ examples.

Reciprocal channel-compatibility conjecture. If these two POVMs are compatible for every pair of orthonormal bases $\mathbf e$ and $\mathbf f$, then $\Phi$ and $\Psi$ are compatibl…

Symmetric denominator implication. If, for every cluster $\mathbf{x}$ containing $x$, ${\mathcal L}(x',\mathbf{x})$ has no $x$ in its denominator, then, for every cluster…