Past exam of the laser science and quantum information processing course of the University of Oxford / 2019 / 4 / d / i

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. ThereforeThe probability to read the entire independently encoded $n$-bit check number correctly by this strategy is $(3/4{)}^n$.