 Solution

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

H ∣ + ⟩ = ∣0 ⟩

and

H ∣ - ⟩ = ∣1 ⟩

. The result probabilities are

p_{+} = \frac{∣ α + β ∣ ^{2}}{2}, p_{-} = \frac{∣ α - β ∣ ^{2}}{2} .

H

followed by

M_{Z}

. If the measured qubit survives and should be left in the original X eigenstate, append a second

H

after the nondestructive

M_{Z}

. The resulting instrument has Kraus operators

H P_{0} H = ∣ + ⟩ ⟨ + ∣

and

H P_{1} H = ∣ - ⟩ ⟨ - ∣

, not Z-eigenstate outputs.

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