n Fig. 18.12. Now I shall explain why the whole circuit shown in Fig. 18.12 is equivalent to a distributed CNOT or C14 gate, which uses Alice's qubit 1, or |a), as the control, and Bob's qubit 4, or /x), as the target. Call /Vii) the initial qubit pairs, labeled by i, j. Hence, V14 = |ax) (tensor state) and 4/23 = 1Boo) (entangled state). Call |0+)23, |1+)23, or |0+), |0-), |1+),|1-), for simplicity, the post- measurement states generated by Alice and Bob's measurements on the qubit pair 2 and 3. The demonstration of the circuit equivalence into a C14 gate holds into the ad-hoc See: Y.-F. Huang, X.-F. Ren, Y.-S. Zhang, L.-M. Duan, and G.-C. Guo, Experimental teleportation of a quantum controlled-NOT gate. Phys. Rev. Letts., 93 (2004), id. 240501; see: http://arxiv.org/abs/quant-ph/ 0408007. Qubit measurements, coding, and teleportation formula: C34C12(1414) Q (18.28) The proof of this equation is left as a tedious, yet relatively easy exercise. From the background of quantum teleportation we have gained in the previous section, and taking the result for granted, the interpretation is, however, straightforward. Indeed, assume for instance that Alice and Bob's measurements result in the 2-3 state collapse into |0+), yielding the cbits 0, 0. The result indicates that the 4-qubit output is |0+) C14/1/14) and, in particular, that the qubit pair 1 and 4 is C14/4/14) = (CNOT|ax) = |a,a x x). Alice does not know Bob's target qubit /x), and Bob does not know Alice's control qubit |a), but both know for certain that the CNOT operation has been duly executed. Likewise, in the case of a |0-) collapse, it is found from the formal proof that the output is X4C14|1/14), with X4 being carried upon the qubit 4, hence the need to apply X again on this qubit (recalling that X2=I), = to transform the result into C14/1/14). The same reasoning applies to the other two collapse cases |1+) and |1->. In summary, the above description exemplifies that it is possible to achieve the quan- tum teleportation of a CNOT gate, with the only resou