R\'enyi-2 entanglement of purification of the symmetric Werner state

arXiv:2611.00144v1 Announce Type: new Abstract: This paper determines exactly the R\'enyi-2 entanglement of purification of the normalized symmetric Werner state in every local dimension $d\ge2$ \begin{equation} \mathrm{EoP}_2(W_{+,d})=\log_2\frac{4d(d+1)}{d^2+3d+4}. \end{equation} We establish additivity for tensor power and, more generally, additivity for finite products of symmetric Werner states with different local dimensions. A canonical purification and its products achieve these values globally, even when arbitrary joint purifications with unrestricted finite dimensional auxiliary systems are allowed.