Past exam of the computer science course of the University of Oxford / 2021 / Quantum information / 2 / c / i / Solution

Either experiment is possible. In the sequential experiment choose $U=X$. The first computational basis measurement on $I/2$ returns a uniform bit $j$ and prepares $|j⟩$. The Pauli X gate changes it to $|1-j⟩$, so the second result is always opposite. The two possible records have probabilities $\mathrm{Pr}(0,1)=\mathrm{Pr}(1,0)=1/2$.

In the two-qubit experiment choose the fixed pure stateThe Born rule gives the same two possible records, again with probability $1/2$ each. The observed computational basis anticorrelation alone does not identify whether the correlation was generated sequentially or shared between two qubits.