Local channels preserving maximal entanglement or Schmidt number
  Maximal entanglement and Schmidt number play an important role in various quantum information tasks. In this paper, it is shown that a local channel preserves maximal entanglement state(MES) or preserves pure states with Schmidt number $r$($r$ is a fixed integer) if and only if it is a local unitary operation. 
Yu Guo, Zhaofang Bai and Shuanping Du
quant-ph math-ph math.FA math.MP