7 problems

Clifford bound conjecture. The cardinality of any unitary 2-design is at least

Let $W_2$ denote the two-anyon-pair state, and let $\Sigma_2$ be a genus-$2$ handlebody. The Clifford group orbit of $W_2$ is represented by removing two solid tori from the interi…

Normal-subgroup conjecture. When $n\geq 3$, the $n$-qubit Pauli group $\mathcal{P}_n$ is the only non-trivial proper normal subgroup of $\mathcal{C}_n$.

Faithfulness conjecture. The matrix representation $\mathcal{M}_{2^n}$ for $\mathcal{C}_n$ is faithful.

Integrality and self-duality conjecture. The entries in the character table of $\mathcal{C}_n$ are integers, and hence all irreducible characters of $\mathcal{C}_n$ are self-dual.

Fix $t$ and let $n$ be sufficiently large. Let $C_{\mathbf{1}_t}$ be the code space appearing in the construction, let $T'$ be the associated symplectic space, let…

Let $U_{\mathcal{Z}}$ be the Zauner unitary associated with the Zauner symplectic matrix … A Weyl–Heisenberg SIC fiducial is a fiducial vector generating a symmetric informationall…