Entanglement Polytopes
summary
Characterizes which collections of single‑site spectra arise from globally pure multipartite states: for each SL‑orbit closure the image of the map sending a state to its stacked local eigenvalues is a convex entanglement polytope, computable by highest‑weight/Young‑diagram data via moment map geometry and invariant theory. Examples: two‑party reduces to matching spectra, three qubits split GHZ/W polytopes, four qubits give a finite catalogue (~12 families). Observes physical ground states approach but do not exactly hit facets — the open question is quantitative facet pinning stability (how close implies sparse preimage).
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