Abstract: Stabilizer states are a convenient and well-studied class of quantum states, with many applications including quantum error correction. One reason why they may NOT be good toy models of holographic systems is that they do not generally obey the constraints on entanglement entropies, which are implied by the Ryu-Takayanagi proposal. (Such constraints are collectively known as the holographic entropy cone; the most commonly known holographic entropy constraint is the monogamy of mutual information.) In this talk, I turn this putative problem on its head by inspecting those stabilizer states, which violate the monogamy of mutual information and other holographic constraints. I identify a sharp common feature among states whose entropies are incompatible with holography: their stabilizing operators form syzygies (“relations among relations”). Extrapolated away from stabilizer states to holographic duality, a syzygy appears to be associated with a violation of locality.