Multipartite superadditivity of quantum relative entropy
= Multipartite superadditivity of quantum relative entropy
Repeated application of <superadditivity of quantum relative entropy> gives
$$
D(\rho_{1\ldots n}\|\sigma_1\otimes\cdots\otimes\sigma_n)
\geq\sum_{j=1}^nD(\rho_j\|\sigma_j).
$$