Suppose Alice starts with two qubits in the Bell state 1/√2 (|00> + |11>) and teleports these qubits to Bob by applying the quantum teleportation protocol to each qubit separately.
(a) What is the state of the two qubits received by Bob?
|00> =
|01> =
|10> =
|11> =
(b) How many classical bits did Alice send to Bob?
a)00> = 1/sqrt2
|01> = 0
|10> = 0
|11> =0
b) 4
a)00> = 1/sqrt2
|01> = 0
|10> = 0
|11> = 1/sqrt2
b) 4
Does anybody got the right answer for this?
The 2 comments above seem wrong
The March 9 comment is right.
To determine the state of the two qubits received by Bob, we need to go through the steps of the quantum teleportation protocol for each qubit:
Step 1: Entangle the two qubits
Alice starts with two qubits in the Bell state:
|Ψ> = 1/√2 (|00> + |11>)
Step 2: Perform a Bell measurement
Alice performs a Bell measurement on her two qubits and her own qubit that she wants to teleport. The Bell measurement consists of applying the CNOT gate to the two qubits she wants to teleport and then applying the Hadamard gate to the first qubit, followed by measuring both qubits.
The CNOT gate acts on the first qubit as the control and the second qubit as the target. The Hadamard gate acts on the first qubit.
If Alice's qubit is in state |0>:
Applying CNOT: |Ψ> = 1/√2 (|0> ⊗ |0> + |1> ⊗ |0>)
= 1/√2 (|00> + |10>)
Applying Hadamard: |Ψ> = 1/2 (|00> + |10> + |01> - |11>)
If Alice's qubit is in state |1>:
Applying CNOT: |Ψ> = 1/√2 (|0> ⊗ |1> + |1> ⊗ |1>)
= 1/√2 (|01> + |11>)
Applying Hadamard: |Ψ> = 1/2 (|00> - |10> + |01> + |11>)
So, depending on the state of Alice's qubit, Bob's two qubits will be in one of the following states:
|00> = 1/2 (|00> + |10> + |01> - |11>)
|01> = 1/2 (|00> - |10> + |01> + |11>)
|10> = 1/2 (|00> + |10> - |01> + |11>)
|11> = 1/2 (|00> - |10> - |01> - |11>)
Now, let's move on to the second part of your question:
To determine how many classical bits Alice sent to Bob, we need to analyze the information flow in the quantum teleportation protocol. In Step 2 of the protocol, when Alice performs the Bell measurement, she measures two qubits. This measurement yields two classical bits of information. One bit is obtained from the measurement outcome of the Hadamard gate, and the second bit is obtained from the measurement outcome of the CNOT gate.
Therefore, Alice sends two classical bits of information to Bob during the quantum teleportation process.