We describe quantum theory by using a complex valued random signal, which is (coherently) averaged over a time window, and a photon click is defined as the energy of this averaged signal surpassing a detector threshold. The random signal is modeled as white noise but grows over time s (proportional to √8). Eventually this random signal will lead to a detector "click" defined by a detector threshold condition, at which point the random signal is reset. Further we proceed by analysing correlations and finally by modeling the quantum state of an entangled pair by a complex valued correlation function.
Andrei Yu. Khrennikov,
"Role of detectors and their proper calibration in inter-relation between classical and quantum optics," Optical Engineering 51(6), 069001 (11 June 2012). https://doi.org/10.1117/1.OE.51.6.069001