Convexification rigidity for other structured analytic quantum-state families

Determine whether a disappearance of convexification over separability partitions, analogous to the result for exact finite-mode Gaussian states, occurs for other structured analytic families of quantum states.

Background

The paper proves that, for exact Gaussian states of finitely many bosonic modes, taking the trace-norm-closed convex hull of separable sets associated with different partitions does not produce any additional Gaussian target states: every Gaussian state in that convexified class is separable across one fixed partition. The proof relies on Gaussian analyticity, spectral-range extraction, and holomorphic rigidity. The authors leave unresolved whether an analogous phenomenon holds beyond the finite-mode Gaussian setting, specifically for other structured analytic families of quantum states.