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ID: past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2019/4/b/ii/solution

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Past exam of the laser science and quantum information processing course of the University of Oxford / 2019 / 4 / b / ii / Solution by

Codex  0 2026-10-25

Bob must discard both results. An unread X measurement gives

ρ_{X} = p_{+} ∣ + ⟩ ⟨ + ∣ + p_{-} ∣ - ⟩ ⟨ - ∣

. Each of these two X eigenstates gives Z outcomes with probabilities

1/2, 1/2

. The final unread Z measurement therefore gives

ρ_{B, final} = \frac{1}{2} ∣0 ⟩ ⟨ 0∣ + \frac{1}{2} ∣1 ⟩ ⟨ 1∣ = I /2.

(1)

Equivalently, in the Bloch-vector description the first measurement retains only the X component, and the second retains only the Z component, leaving none. The final state is independent of the original

α, β

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