Hybrid second-order coherence in a time-reversed Young's experiment

We develop a quantum-optical theory of the operational second-order correlation function underlying the time-reversed Young's experiment with a scanned point emitter and a fixed single-pixel detector. By embedding the source coordinate in an auxiliary Hilbert space with a position projector, we show that the empirical correlator can be written as a genuine Glauber-type $G^{(2)}$ that correlates a one-channel field intensity with a position projector, with projector idempotence ensuring that it remains second order. Evaluated in the time-reversed Young geometry, this hybrid field-plus-label correlator reproduces deterministic diffraction-free fringes and captures ghost imaging, imaging with undetected photons, and related schemes.