Physical $\sigma_x$ swaps $A^0$ and $A^1$. Direct multiplication of the four blocked matrices shows
$$
A^{1-i_1}A^{i_2}
=\sigma_x(A^{i_1}A^{i_2})\sigma_x,
$$
$$
A^{i_1}A^{1-i_2}
=\sigma_z(A^{i_1}A^{i_2})\sigma_z.
$$
Thus one may choose
$$
\boxed{V_a=\sigma_x,\qquad V_b=\sigma_z}.
$$

Solved by gpt-5.6-sol high.


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-343/3/b/i/solution