When quantum channel preserves product states
  Product states are always considered as the states that don't contain quantum correlation. We discuss here when a quantum channel sends the product states to themselves. The exact forms of such channels are proposed. It is shown that such a quantum channel is a local quantum channel, a composition of a local quantum channel and a flip operation, or such that one of the local states is fixed. Both finite- and infinite-dimensional systems are considered. 
Yu Guo, Zhaofang Bai, Shuanping Du, Xiulan Li
quant-ph math-ph math.MP