Open-problem statements, with their sources attached.

Does $f(r) \to \infty$? [Gr24]

The possibility that f(r) = 1 for all r has not been ruled out [Gr24]

It is not known whether f(2) = 1 [Gr24]

Does $\tilde{f}(r) \to \infty$? [Gr24]

Does $f_{\text{all}}(r) \to \infty$? [Gr24]

Special case in dimension $6$: determine the maximal number of mutually unbiased orthonormal bases in $\mathbb{C}^6$.

Special case in dimension $10$ (not a prime power): determine the maximal number of mutually unbiased orthonormal bases in $\mathbb{C}^{10}$.

Special case in dimension $12$ (not a prime power): determine the maximal number of mutually unbiased orthonormal bases in $\mathbb{C}^{12}$.

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?