9 problems

Classification conjecture. Any MUB-triplet $(X_1,X_2,X_3)$ in dimension $d=6$ is permutationally unitary equivalent to an MUB-triplet obtained by the construction $(\mathrm{hff})$.…

Szöllősi-family non-extendability conjecture. Any matrix $S\in X(\alpha)$ in the Szöllősi family cannot be part of an MUB-quadruplet.

Let $U(d)$ be the unitary group, let $\nu$ be normalized Haar measure on $U(d)$, let $e$ be its identity, and let $\mu_{[\bm H]}$ be the smoothed measure associated with the equiva…

Let $U(d)$ be the unitary group, let $H(d)$ be the set of complex Hadamard matrices in $U(d)$, and let $B(d)$ be the optimal positive-definite-functions upper bound for mutually un…

A set of mutually unbiased bases (MUBs) in $\mathbb{C}^{2^m}$ is strongly $\mathbb{C}$-unextendible if no additional basis can be added even after allowing the bases to be changed…

Let a 2-design in dimension $d$ be a finite projective 2-design, and let a SIC denote a symmetric informationally complete measurement while an MUB denotes a complete set of mutual…

Let $n$ be a positive integer. A type-I complementary array over the alphabet ${0,1,-1}$ is an array represented by a function $f_{n-1,0}({\bf{x}})$, with the indices and parameter…

Let $H_1$ be any complex Hadamard matrix of order $6$, not equivalent to the isolated matrix $S_6$. Let $g_1$ be the function defined by the source's equation, and let $\rho$ be an…

Let $X$ be a normalized uniformly distributed random vector. For mutually unbiased bases, let $m_1,m_2,\ldots,m_k$ denote the relevant maximum second-moment quantities, and let…