measurements and Xn, Xn' Zn, Zn' are Pauli gates controlled by classical bits n, m, n'm'. The inputs /q/1, 19'16 are two qubits from Alice, who accesses the quantum wires 1, 2, 5, and 6. Bob only has access to the quantum wires 3 and 4, where he retrieves the teleported qubits under the tensor state 1/s/ : CNOT|q)319')4 = C43|9)3 x as illustrated in Fig. P1 (applying a second CNOT, allowing Bob to retrieve Alice's individual qubits /9)3, (9')4). For the teleportation, Alice and Bob share a 4-qubit entangled state 1x), defined by + + + (the circuit used to generate 1x), which entangles two Bell states 1Boo) is shown in Fig. 18.11). We proceed now to the formal demonstration of the 2-qubit teleportation effect that is achieved through the above-described circuit. To analyze the qubit evolution in pre- and post-measurement stages, we need first to detail the Bell-state measurement circuits B, B'. Such circuits are shown in Fig. 18.5, and reproduced in Fig. P2 according to the circuit notations. In the figure, the term Cij designates CNOT gates where i is the control qubit, j is the target qubit, and Hk are Hadamard gates placed on the quantum wire k. The two Bell-measurement apparatuses B, B' output the post-measurement classical bits n, m and n'm', respectively, which correspond to pure states \nmn'm') 1256, to be defined later. Our task now is to calculate the 6-qubit state situated just past the two Hadamard gates in B, B' and ahead of Alice's two measurements. This will allow us to know what post- measurement states \nmn'm') 0/*/23 are to be expected, and hence, the action of the Xn, Xn', Zn, , Zn' gates based on Bob's knowledge of the four classical bits n, m, n'm'. D. Gottesman and I.L. Chuang, Quantum teleportation is a universal computational primitive. Nature, 402 (1999), 390-3, ,http://arxiv.org/PS_cache/quant-ph/pdf/9908/9908010v1.pdf. Appendix P q'> 6 Figure P1 Six-qubit quantum circuit for teleporting two qubits. Figure P2 Principle of Bell measurement or measurement in Bell state. We then define Alice'