  We derive an extension of the quantum regression theorem to calculate
out-of-time-order correlation functions in Markovian open quantum systems.
While so far mostly being applied in the analysis of many-body physics, we
demonstrate that out-of-time-order correlation functions appear naturally in
optical detection schemes with interferometric delay lines, and we apply our
extended quantum regression theorem to calculate the non-trivial photon
counting fluctuations in split and recombined signals from a quantum light
source.
