No-cloning with unitary scaling

It is known that the classical information like strings of bits can be copied. In 1982, Wootters and Zurek proposed the quantum no-cloning principle. No-cloning principle says that it is impossible to make an identical copy of an arbitrary unknown quantum pure state by using unitary evolution. In this paper, we call U $\mathrm{\mid }\psi >$, where U is any unitary operator, a U-copy of the state $\mathrm{\mid }\psi >$ and show it is impossible to make a U-copy of an arbitrary unknown quantum pure state by using unitary evolution.