7 problems

Consider the phaseless stabilizer StateHSP and stabilizer state cloning tasks, for which the paper establishes worst-case lower bounds. Average-case extension conjecture. The worst…

A graph state is a stabilizer state associated with a graph, and two stabilizer states are LU-equivalent if they differ by a tensor product of single-qubit unitary operators, while…

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…

Approximate stabilizer-state conjecture. There exist a pure stabilizer state $\phi_{stab}$ and a constant $c$ independent of $n$ such that

For each $n$, let the $n$-party hypergraph cone be the cone of entropy vectors obtained from $n$-party hypergraphs, and let the $n$-party stabilizer cone be the cone of entropy vec…

Let two stabilizer states be given. They are local unitary equivalent if there exists a product of unitary operators, one acting on each qubit, that maps one state to the other; th…