Two-Tooth Bosonic Quantum Comb for Temporal-Correlation Sensing

We characterize the causal structure of coherence transport in open bosonic systems using a two-tooth quantum comb. We show that, by mapping sequential interactions between a structured bosonic absorber and a long-lived coherent probe onto a process-tensor description, the probe functions as a temporal interferometer for environmental two-time correlations. We derive closed-form expressions for a nonmonotonic memory response arising from a competition between instantaneous thermal responsivity and the delay-dependent evolution of absorber correlations. By tuning the intertooth delay, the comb can enhance or suppress the net temperature imprint, providing direct access to population correlators and enabling discrimination of spectrally structured non-Markovian fluctuations from effective thermal noise. The protocol provides an explicit bosonic implementation of two-time thermal-correlation sensing, complementary to prior studies of memory effects in noisy quantum metrology.