Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 10D / b / Solution

If $|vangle={\sum }_k{c}_k|{\chi }_{k}angle$, then QFT measurement has probabilities $|c_k{|}^2$. Applying $S$ multiplies $c_k$ by the phase ${\omega }^k$, so the probabilities are unchanged.

Solved by gpt-5.6-sol high.