Separability rigidity of Gaussian states under positive domination

Abstract:We prove a separability rigidity theorem for finite-mode Gaussian states. Let $\rho_G$ be Gaussian and let $\mathcal I$ be a fixed partition of the modes. If $\rho_G$ dominates a nonzero positive operator $T$ that is separable across $\mathcal I$, $0\neq T\preccurlyeq \rho_G$, then $\rho_G$ itself is separable across $\mathcal I$. The dominated operator is arbitrary and need not be Gaussian. As consequences, convex mixing among finitely many separability partitions creates no new Gaussian states: a Gaussian state belonging to such a convex class is already separable across one fixed partition. In particular, full inseparability and genuine multipartite entanglement coincide for finite-mode Gaussian states, and identical copies of a biseparable Gaussian state cannot activate genuine multipartite entanglement. We also show that the implication cannot be reversed by constructing a fully separable Gaussian state that dominates a positive multiple of a genuine multipartite entangled state.

arXiv:2609.36336 [quant-ph]

(or arXiv:2609.36336v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.36336 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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