 Solution

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

Assume Alice independently chooses X or Z with equal probabilities and that bit labels

0, 1

identify the corresponding positive and negative eigenstates. If Daisy measures Z, she reads a Z-encoded bit correctly with probability one and an X-encoded bit correctly with probability one half. Therefore

P (correct bit ∣ M_{Z}) = \frac{1}{2} \cdot 1 + \frac{1}{2} \cdot \frac{1}{2} = \frac{3}{4} .

The probability to read the entire independently encoded

n

-bit check number correctly by this strategy is

(3/4)^{n}

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