 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2021/quantum-information/2/c/ii/solution

Either experiment is again possible. The sequential experiment with

U = I

repeats its first measurement outcome in every basis: the first projective measurement has prepared one of that basis's eigenstates, and the identity leaves it unchanged.

For the two-qubit experiment choose

∣ ψ ⟩ = ∣ Φ^{+} ⟩ = \frac{∣00 ⟩ + ∣11 ⟩}{2} = \frac{∣ ++ ⟩ + ∣ -- ⟩}{2} .

The two expansions exhibit identical outcomes in both specified bases. Each allowed equal-label record has probability

1/2

. These are fixed choices of

U

and

∣ ψ ⟩

, respectively; neither depends on which of the two bases Alice selects.

 New to topics? Read the docs here!