Local extrema of entropy functions under tensor products
  We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed under tensor products if one of the subspaces has dimension 2. 
Shmuel Friedland, Gilad Gour, Aidan Roy
math-ph math.MP quant-ph