7 problems

Strange-state discrimination conjecture. With the assistance of sufficiently many copies of the Strange state, this ensemble can be perfectly distinguished using a PWF POVM.

Mana-maximization conjecture. Based on numerical results, stabilized subspaces of finite subgroups of the Clifford group whose Wigner functions are everywhere non-vanishing maximiz…

Single-qutrit count conjecture. The total number of maximal magic states of the single-qutrit system is $45$.

WH-MUB bound conjecture. The quantity $M_\alpha(|\psi\rangle)$ is bounded by the bound with $\Delta=0$, and equality is attained uniquely by the WH-MUB fiducial states.

Three-qubit exhaustion conjecture. This set exhausts all maximal magic states in the three-qubit system.

WH-MUB optimality conjecture. WH-MUBs saturate the optimal bound for general $n$-qubit systems, except when $n=1$ or $n=3$.

Let $\ket{\rm Hog}$ be a 3-qubit Hoggar state, obtained from the fiducial state $\ket{\rm Hog_0} \propto (-1+2i,1,1,1,1,1,1,1)^T$ by the action of the Pauli group. Let…