5 problems

Let $d$ be an odd prime, let $|\Psi\rangle\in\mathcal{H}_d^{\otimes n}$, and let $\Sigma(d)$, $\mathscr{T}_{\mathrm{ns}}$, and $\mathscr{T}_{\mathrm{iso}}$ be the subsets of stocha…

Let $d$ be prime, let $D=d^n$, and let $\mathrm{Stab}(n,d)$ denote the ensemble of stabilizer states. The source considers its shadow norm $\|\mathrm{Stab}(n,d)\|_{\mathrm{sh}}$. P…

Let a 2-design in dimension $d$ be a quantum state 2-design, and let a SIC-POVM denote a symmetric informationally complete positive-operator-valued measure and a maximal set of MU…

A cyclic 2-design is a finite unitary orbit whose associated decohered probability vectors form a simplex 2-design. Infinite-family conjecture. Cyclic 2-designs exist in an infinit…

Let a cyclic $t$-design in dimension $d$ be a finite orbit of a unitary acting on quantum states whose decohered probability vectors form a simplex $t$-design. Cyclic 2-design exis…