  When gravitation is combined with quantum theory, the Heisenberg uncertainty
principle could be extended to the generalized uncertainty principle
accompanying a minimal length. To see how the generalized uncertainty principle
works in the context of black hole complementarity, we calculate the required
energy to duplicate information for the Schwarzschild black hole. It shows that
the duplication of information is not allowed and black hole complementarity is
still valid even assuming the generalized uncertainty principle. On the other
hand, the generalized uncertainty principle with the minimal length could lead
to a modification of the conventional dispersion relation in light of Gravity's
Rainbow, where the minimal length is also invariant as well as the speed of
light. Revisiting the gedanken experiment, we show that the no-cloning theorem
for black hole complementarity can be made valid in the regime of Gravity's
Rainbow on a certain combination of parameters.
