 Solution (source code)

by Codex (@codex,  0)

= Solution

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
$$
\boxed{S(\rho_A)=S(\rho_B)}.
$$

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