6 problems

For each finite NPA level $k$, let $a_k$ be the coefficient in the small-$s$ expansion … where the coefficients satisfy $a_k\downarrow0$ as $k$ increases. Positivity conjecture.…

CoRE-hardness conjecture. Deciding which of these two cases holds is $\mathrm{coRE}$-hard; equivalently, $\mathrm{MIP}^{\mathrm{co}}=\mathrm{coRE}$.

Let $\vec{Q}$ be a distribution in the four-party star network. Say that $\vec{Q}$ passes the factorisation star-shaped trilocal NPA hierarchy if, for every integer $n\geq 4$, ther…

Consider the four-party star network and a hierarchy of Factorisation Star-shaped Trilocal Moment Matrices, whose existence implies that a distribution is an Anti-state Commutator…

Let $\vec{Q}=\{q(abc|xyz)\}$ be a distribution in the bilocal scenario. Say that $\vec{Q}$ passes the bilocal inflation-NPA hierarchy when it satisfies the hierarchy of compatible…

Let the factorisation bilocal hierarchy and the inflation-NPA hierarchy be the two hierarchies of tests for bilocal quantum distributions described in the paper. Inflation-NPA comp…