= Solution
<Outcome determinism> means that a complete hidden state $\lambda$, together with the chosen measurement settings, fixes each outcome. The observed <probabilities> can still arise from an ensemble of unknown $\lambda$. This differs from deterministic unitary evolution of a <wavefunction>, which does not by itself specify a unique measurement outcome. <Quantum nonlocality> means failure of a Bell-local account of the correlations, under assumptions including <measurement independence>; it is stronger than the existence of entanglement and does not imply controllable faster-than-light signaling.
Use the first ket for the <Positron> and the second for the <electron>. Before either final <beam splitter>, the first pair of splitters and annihilation produce
$$
|\Psi\rangle=-\frac12|\gamma\rangle
+\frac i2|u^+v^-\rangle+\frac i2|v^+u^-\rangle+\frac12|v^+v^-\rangle.
$$
The <photon> state $|\gamma\rangle$ is orthogonal to the surviving charged-particle sector. Its <probability> is $1/4$, while the remaining sector has squared norm $3/4$. The states below retain that <photon> amplitude and are normalized over \b[all trials], without conditioning on nonannihilation. For compactness write $|cc\rangle=|c^+c^-\rangle$, and similarly for $|cd\rangle,|dc\rangle,|dd\rangle$.
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