# Strong subadditivity Strong subadditivity (SSA) states that $ S\left(\rho_{A B C}\right)+S\left(\rho_C\right) \geqslant S\left(\rho_{A C}\right)+S\left(\rho_{B C}\right), $where $\rho_{B C}=\operatorname{Tr}_A \rho_{A B C}$ etc. It is a property that all quantum systems satisfy. It can be derived using e.g. data processing inequality as in [[2022#Hollands (Lectures)]]. In holography, it can be shown that SSA is satisfied for [[0007 RT surface|HRT]] surfaces, assuming [[0480 Null energy condition|NEC]] in [[0554 Einstein gravity|Einstein gravity]]. ## Refs - [[LiebRuskai1973]] proof ## Relation to conditional entropy - strong subadditivity of vN entropy $\leftrightarrow$ concavity of [[0276 Conditional entropy|conditional entropy]]