= Exact pure-state overlap readout would allow superluminal signalling
{title2=$|\langle0|\psi\rangle|^2\in\{0,1\}\ \text{or}\ \{1/2\}$}
With a fixed reference $|0\rangle$, exact overlap readout on Bob's remotely prepared state distinguishes the computational basis from the diagonal basis in one use, by the displayed disjoint squared-overlap sets. This would reveal Alice's spacelike basis choice. The argument rules out even deterministic exact overlap magnitude, avoiding the additional unphysical global-phase dependence of a raw complex inner product.
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