Alice measures Alice measures Bob's 1-qubit Xm' Zm a|0) + B|1) a|1) + B|0) a|0) - B|1) a|1) - B|0) In the last expression in the right-hand side, the first two qubits, which are controlled by Alice, and the last qubit, which is Bob's, have been regrouped for clarity. Then come Alice's measurements of the first two qubits, with the corresponding classical-bit results m, m' (respectively) obtained at 4. The rule has it that Alice must communicate the two classical bits, or cbits, m, m' to Bob. It is clear that if Alice measures |00), the system state collapses into the qubit |00) >(a|0) + B|1)), as shown in Eq. (18.23), and SO on for each of the four possible measurements. The outcomes of Alice's measurements, and the resulting state of Alice and Bob's qubits, are summarized in Table 18.3. The two cbits m, m' communicated to Bob make it possible to define the gates Xm' Zm on Bob's wire (Fig. 18.7), as also shown in Table 18.3. It is seen from the table that in the first case (Alice measures |00)) Bob's qubit has collapsed into the state 1q) = x|0) + B|1). Thus, Alice's original qubit |q) has been successfully "teleported" to Bob. From the two cbits m, m' = 0, 0, Bob is, thus, instructed to use the gates X°Z° = I, namely, to leave his qubit unchanged. In the second case (Alice measures |01)), Bob's qubit is a|1) + B|0), and the application of X°Z¹ = Z swaps the amplitudes a, B to yield |q) = a|0) + B|1). The last two cases are also straightforward to analyze. The principle of QT can, thus, be summarized as follows: (a) Because Alice and Bob share an ERP-Bell state, Alice's measurements cause the system to collapse and condition Bob's qubit; (b) Alice communicating the two classical bits describing her measurement makes it possible for Bob to retrieve Alice's qubit lq). Remarkably, Alice has no knowledge of the teleported |q). This point is quite important. Indeed, if Alice had this knowledge, she could communicate to Bob the full information required (amplitudes, base) for him to re-create the same qubit locally, an