Past exam of the laser science and quantum information processing course of the University of Oxford / 2017 / 5 / b / Solution

Before the gates, write the two Bell states asThe CNOT gate sends the last bit to $b\oplus a$. Projection onto outcome 0 on qubit 4 therefore requires $b=a$. After the Hadamard gate on qubit 2, projection onto its outcome 0 contributes $1/\sqrt{2}$ for either remaining value of $a$. The unnormalized surviving state isThusThis is entanglement swapping: photons 1 and 3 become entangled even though the joint measurement acts only on their original partners.