Comment on "Stronger subadditivity of entropy" by Lieb and Seiringer   math-ph/0412009
  We show how recent results of Lieb and Seiringer [math-ph/0412009; Phys. Rev. A 71, 062329 (2005)] can be obtained from repeated use of the monotonicity of relative entropy under partial traces, and explain how to use their approach to obtain tighter bounds in many situations. 
Mary Beth Ruskai