Open-problem statements, with their sources attached.

Open benchmark statement: does an $\mathrm{AME}(8,4)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(8,6)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(8,10)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(9,6)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(9,10)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(10,6)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(10,10)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(11,3)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(11,4)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(11,6)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(11,10)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(12,5)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(12,6)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(12,10)$ state exist?

Open Quantum Problem 35: classify all pairs $(n,d)$ with $n \ge 2$ and $d \ge 2$ for which an $\mathrm{AME}(n,d)$ state exists.

For $N = 6$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 6$ and $D = 4$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 6$ and $D = 5$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 6$ and all $D \geq 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?

For $N = 8$ and $D = 3$, does there exist no solution to the monochromatic quantum graph equation system over $\mathbb{C}$?