A simple proof of the strong subadditivity inequality
  Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57--65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics. 
Michael A. Nielsen and Denes Petz