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In Shannon information theory, the capacity of a memoryless communication channel cannot be increased by the use of feedback. In quantum information theory, the no-cloning theorem means that noiseless copying and feedback of quantum information cannot be achieved. In this correspondence, quantum feedback is defined as the unlimited use of a noiseless quantum channel from receiver to sender. Given such quantum feedback, it is shown to provide no increase in the entanglement-assisted capacities of a memoryless quantum channel, in direct analogy to the classical case. It is also shown that in various cases of nonassisted capacities, feedback may increase the capacity of memoryless quantum channels.