Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 49 / 1 / b / Solution

If there is no marked entry, the Boolean quantum oracle is the identity. The uniform superposition state is a positive eigenstate of the Grover diffusion operator:Thus every iteration leaves the full state $|s⟩\otimes |-⟩$ unchanged. The measured search bits have the uniform distributionOnly the first $n$ qubits are measured in the printed circuit. If the untouched ancilla were also measured in the computational basis, its bit would be an independent fair bit, giving probability $1/(2N)$ for each joint outcome.