Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 343 / 3 / d / i

In the X eigenbasis, $M$ is $\mathrm{diag}(I,X)$ on its physical indices. A physical X insertion changes the sign of the minus block and can be pulled through asConjugating both physical legs by Z swaps the two blocks:Hence

Likewise $N=\mathrm{diag}(I,Z)$. Its analogous relations are

Solved by gpt-5.6-sol high.