7 problems

Horodecki's conjecture. The Werner state $\rho_{\alpha}$ is $n$-undistillable for every $n\in\mathbb{N}$ if and only if $\alpha\geq-\frac{1}{2}$.

Smallest-measurement-number conjecture. The smallest number of measurements $n$ such that

A Werner state is a bipartite quantum state of the form … with $t\in[-1,1]$. A state is distillable if entanglement can be extracted from it by entanglement distillation protocols;…

Consider the diagram-based construction of mixed Werner states using products of the states $C_U$ indexed by non-intersecting polygon diagrams. General construction conjecture. The…

Let ${\cal D}$ range over the partition diagrams of $\{1,2,\ldots,n\}$, let $\rho_{\cal D}$ be the associated diagram states, and let $\Delta_{\cal D}=\prod_{U\in{\cal D}}\Delta_U$…

2-distillability conjecture for Werner states. None of the Werner states $\rho_W(t)$, $t\in(1/d,1/2]$, is $2$-distillable.

Werner-state nondistillability conjecture. None of the Werner states $\rho_W(t)$, $t\in(1/d,1/2]$, is distillable.