Holographic entropy inequalities for six regions
In plain words
Entanglement between regions of a holographic system obeys special inequalities that general quantum systems need not obey. The full list is known only up to five regions.
Precise statement
For n boundary regions, the Ryu-Takayanagi entropies of all $2^n - 1$ unions form a polyhedral cone (Bao et al. 2015). Determine the complete list of facets (holographic entropy inequalities) for $n = 6$; the cone is known for $n \le 5$.
What would settle it
A complete list of $n = 6$ facets with a proof that each is valid and tight and that no others exist.
Status in the literature
Unverified note
$n = 5$ was completed in 2019; 2024-2026 work computed extreme rays of the 6-party strong-subadditivity-compatible cone and applied reinforcement-learning searches, without a complete 6-party facet list.