Question

Consider the two-qubit Bell state l'1*) = 101) +110)) shared by Alice and Bob. Alice also possesses an additional qubit, in state lx) = a10) +이 1), with lal2+b21. Alice's goal is to teleport state lx) to Bob (neither of the two is assumed to know the values of a and b). The total state of the system a. Assume you do not have direct access to Bell state measurement for Alice's two qubits. Construct the protocol Alice should follow to implement Bell-state measurement on her two qubits using a combination of CNOT, Hadamard, and measurement in the computational basis b. What is the post-measurement state of Bob's qubit for each of the four possible outcomes of Alice's measurement? c. Express the total state of the three qubits in the form where the first two qubits are the ones in Alice's possession and the last one is Bob's, ie, specify the ci and vi d. What is the probability of each of Alice's measurement outcomes? e. Explain why the result from (d) is important in explaining why quantum teleportation does not violate special relativity (information cannot travel instantaneously)? f. What information does Alice give Bob when they communicate classically and which quantum gate does he implement in each case? g. To convey the information in (f), how many classical bits does she need?

please explain

Answer 1

The entangled state is Vertical-bar psi^+ = 1/squareroot 2 ( Vertical-bar 01 + Vertical-bar 10) and the Qubit that Alice wants to teleport is Vertical-bar chi = a Vertical-bar 0 + b Vertical-bar 1 with a^2 + b^2 = 1 The teleportation circuit is given as The step step procedure is that Alice & Bob will have one of the entangled pair and they move far away from each other Now Alice has another Vertical-bar chi which she intends to Teleport so Alice has a pair of bits, the 1^st one is from Vertical-bar chi and the 2^nd one is from the entangled pair Vertical-bar psi Then Alice a (NOT Gate on this pair i.e keeping the 2^nd bit (Target) same if the 1^st bit (control) is 0 and flipping the Target bit if the control bit is 1 Then lice performs a gate operation on her 1^ST Qubit Now gate turns a pure state to a superposed state