Recombination asks a different question of the state, turning the hidden phase relation into a changed outcome budget. The final probabilities are exact only for the stated phase relation and ideal recombination gate; laboratory runs add calibration error, imperfect interference, decoherence, leakage, and readout uncertainty.
A later recombination gate turns the stored phase relation into exact counts. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Recombination turns phase into counts
The recombination stage maps the phased state to the one outcome.
HZ∣+⟩=∣1⟩
The count budget moves only at recombination
The scan separates the hidden phase row from the final row where the measured budget changes.