Strong Subadditivity Inequality and Entropic Uncertainty Relations
Li Gao, Marius Junge, Nicholas LaRacuente · 2017
We prove a generalization of the strong-subadditivity (SSA) inequality in the context of finite dimensional von Neumann algebras. Our generalized SSA inequality subsumes various entropic uncertainty relations, such as the Maassen-Uffink inequality in the presence of quantum memory. Motivated by the generalization of SSA, we introduce an analog of conditional mutual information and discuss superadditivity and monotonicity under certain operations. Our proof uses complex interpolation and noncommutative mixed $L_p$ spaces.