Open-problem statements, with their sources attached.

Special case in dimension $14$ (not a prime power): determine the maximal number of mutually unbiased orthonormal bases in $\mathbb{C}^{14}$.

Special case in dimension $15$ (not a prime power): determine the maximal number of mutually unbiased orthonormal bases in $\mathbb{C}^{15}$.

Open Quantum Problem 13: determine the maximal number of mutually unbiased orthonormal bases in $\mathbb{C}^d$ for $d \ge 2$.

Open benchmark statement: does an $\mathrm{AME}(7,6)$ state exist?

Open benchmark statement: does an $\mathrm{AME}(7,10)$ state exist?

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.