Quantum information is incompressible without errors.

A classical random variable can be faithfully compressed into a sequence of bits with its expected length lying within one bit of Shannon entropy. We generalize this variable-length and faithful scenario to the general quantum source producing mixed states rho(i) with probability p(i). In contrast to the classical case, the optimal compression rate in the limit of large block length differs from the one in the fixed-length and asymptotically faithful scenario. The amount of this gap is interpreted as the genuinely quantum part being incompressible in the former scenario.