through the same projector set Pi=1,2,3,4 as in the bit-flip channel. Clearly, the fidelity characteristics and limitations of the quantum repetition code for the phase-flip channel are strictly the same as in the case of the bit-flip channel. I shall conclude this section by showing an important property, according to which the projector set Pi=1,2,3,4 is not the only tool to perform error syndrome measurements in bit- or phase-flip channels. This will be very useful in the next section, concerning the Shor code. Consider indeed that we have the possibility of performing partial measurements with the aim of comparing qubit pairs. For instance, we may compare the first and the second qubit, or the second and the third, or the first and the third, and SO on. Should any comparison reveal a difference, then an error is detected. One must then perform as many such comparisons as necessary to obtain an unambiguous error syndrome, leading to certain error correction. Let us see how this approach can be implemented. With a 3-qubit bit-flip code, comparing qubit pairs consists of projecting the received state by using the following "observable" operators: I0(100)(001+|11)(11))- (01)(01/+/10)(10|) (24.19) Z13 = (0)00I01)(1+1)(10100)(0). It is clear that the expectation value Zij) = (91Zijla) for any of the above three operators Zij is equal to +1, should the qubits i and j match (no error), while it is equal to - 1, should they not match (error). Let us leave here the consideration of being capable of physically measuring observables, such as +1. The matter is simply that the partial measurement yields two possible logical answers: error or no error on the pair of qubits considered, corresponding to classical YES or NO information. Such information is the key to the elaboration of an error diagnostic, leading to corrective action. Since a single measurement (or YES or NO information) is not sufficient to tell which of the two qubits 24.2 Shor code is actually errored (or flipped), we may perform as many successive measure