Lower bound on the relative error of mixed-state cloning and related   operations
  We extend the concept of the relative error to mixed-state cloning and related physical operations, in which the ancilla contains some a priori information about the input state. The lower bound on the relative error is obtained. It is shown that this result contributes to the stronger no-cloning theorem. 
A.E. Rastegin (Irkutsk State University)