  We study the optimization of any quantum process by minimizing the
"randomness" in the measurement result at the output of that quantum process.
We conceptualize and propose a measure of such randomness and inquire whether
an optimization of the quantum process based on that measure, can reach the
point where the process operates with maximum fidelity. We consider approximate
quantum cloning and teleportation processes, and find, in particular, that the
optimal approximate state-dependent quantum cloning machine obtained by
maximizing the fidelity is different from that obtained by minimizing the
randomness.
