Separable Ball around any Full-Rank Multipartite Product State

Robin Yunfei Wen, Achim Kempf

We show that around any $m$-partite product state ${\rho }_{\mathrm{prod}}={\rho }_1\otimes ...\otimes {\rho }_m$ of full rank (that is $\det ({\rho }_{\mathrm{prod}})\ne 0)$, there exists a finite-sized closed…