5 Quantum teleportation This problem shows how to replicate a quantum state using classical infor- mation plus an entangled pair of qubits. Alice has qubit A, which we can write as @ 10) A + 8|1) A Bob prepares an entangled Bell pair (it doesn't matter which Bell pair, but let's choose the following to be definite) ( 10 ) B 10 ) ( + 11 ) B/1)c ) . The full state of all the qubits is initially 12/) = (a 10) A + 811) 4) 8(10) B 10 ) c + 11) B|1)c) . From his entangled pair, Bob now sends qubit B to Alice and qubit C to Charlie. Alice has a measurement device that will distinguish between the 2 Bell states for qubits A and B, [D' ) AB = 1 V2 (10) 4 10) B + 1) 4 1)B) , 102) AB=(10)41) B+ 11)4 10) B) , 1 (D' ) AB = (10) 4 1) B -1)4 10)B) , 104) AB=- 1 VZ (10) 4 10) B - 11) 4 1) B) . She makes a measurement on her two qubits A and B, and the result is D ) AB. (a) Rewrite 10) 4 10) B, 10) 41) B, 1) 4 10) B, 1) ) B in the basis of Bell pairs D) AB, ') AB, ' ) AB , "AB. (b) Given that Alice measured |4) AB, what state is Charlie's qubit C' in? Now Alice texts Charlie the result of her measurement. Based on this information, he must perform a unitary operation on his qubit to convert it to Alice's initial state a |0) + 8|1). (c) Write down (as a 2 x 2 matrix) the unitary transformation he must perform in this this case. (d) Why doesn't Charlie's replication of Alice's qubit violate the quantum no cloning theorem we proved in the second