obtain: (18.6) Second, the post-measurement state 1q') is q')=12m). (18.7) We may conclude from the two above results that the projective measurement of qubits is essentially similar to the previously described base measurement in the pure states, except that the measurements project the qubit onto the eigenstates of A. Such a conclusion is true, but it fails to convey an important property. Indeed, if we know prior to the measurement that the qubit must be in one of the eigenstates, then we are in the same situation as in the previous pure-state case. No matter whether we use P = 120) (201 or P1 = (21) (A1 for the qubit measurement, we always retrieve a classical 0 or 1 bit. To recall, if we use P when the qubit is in state 120) or P1 when the qubit is in state 121), the measurements are certain to "succeed," yielding the classical 0 or 1 bits, and the collapsed qubit state remains invariant. But if we use the wrong operator (e.g., P when the qubit is 121)), the measurement "fails," and the qubit state is annihilated. However, such a failure indicates that the qubit must have been in the other orthogonal state, and, therefore, we can conclude with certainty the value of the corresponding classical bit. The only penalty in this event is that we have lost the qubit, and it cannot be reused for another quantum computation, for instance as an input to a subsequent quantum gate within a quantum circuit. The key conclusion is that measurements can be destructive (even when informative) and, therefore, it is safer to proceed to quantum measurements only at the end of a purposeful computational chain. If intermediate measurements are required, one must ensure that these are always nondestructive, SO that the collapsed qubit may be reused in the rest of the circuit computation. In quantum-gate circuits (Chapter 16), any quantum measurement is conventionally represented by an "ammeter" symbol, as illustrated in Fig. 18.2. The two output lines shown at the right correspond to the collapsed or post-measurement state (12m)) 