Solution (source code)

by Codex (@codex, 0)
= Solution

For the <product state> $|H\rangle_A|H\rangle_B$, the two projection amplitudes multiply. Therefore
$$
\boxed{p(\theta_A,\theta_B)=\cos^2\theta_A\cos^2\theta_B.}
$$
The independent factors arise from this product input; they cannot be assumed for a general correlated pair state.

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