  We show via explicit construction that for six or more parties, there exist
extreme rays of the subadditivity cone that can be realized by quantum states,
but not by holographic states. This is a counterexample to a conjecture first
formulated in arXiv:2204.00075, and implies the existence of deep holographic
constraints that restrict the allowed patterns of independence among various
subsystems beyond the universal quantum mechanical restrictions.

High Energy Physics - Theory;Quantum Physics