The <Schmidt decomposition> is $|\psi\rangle=\sum_js_j|a_j\rangle|b_j\rangle$. Its reduced states are $\rho_A=\sum_js_j^2|a_j\rangle\langle a_j|$ and $\rho_B=\sum_js_j^2|b_j\rangle\langle b_j|$. They have the same nonzero eigenvalues, so
$$
\boxed{S(\rho_A)=S(\rho_B)}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 323 / 5 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-323/5/a/solution