Computation of sandwiched relative alpha-entropy of two n-mode gaussian states

Abstract

A formula for the sandwiched relative $α$-entropy $\widetilde{D}_α(ρ\vert\vertσ)=\frac{1}{α-1}\, \ln\,{\rm Tr}\, \left(σ^{\frac{1-α}{2α}}\,ρ\,σ^{\frac{1-α}{2α}}\right)^α$