Question
Suppose that Alice would like to teleport a pair of possibly entangled qubits to Bob, label them qubits 1 and 2, in the state ||.
Suppose that Alice would like to teleport a pair of possibly entangled qubits to Bob, label them qubits 1 and 2, in the state ||. Further, suppose that they share two pairs of qubits, both in the state |00|, with the qubits in the first pair labelled 3 and 4 and the qubits from the second pair labelled 5 and 6. So, Alice has qubits 1, 2, 3, and 5, while Bob has qubits 4 and 6. Show that by applying the quantum teleportation protocol twice, first to qubit 1 and the entangled qubits 3 and 4, and then to qubit 2, with qubits 5 and 6, Bob will end up with his two qubits (labelled 4 and 6) in the state ||. This shows that entanglement is preserved under the teleportation protocol. To make the calculation easier, just show that this works in the special case where || = |00| + |11|. As a bonus, do this for the general 2 qubit case.
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