Fig. 3: QKD lasers interference with unstabilized and stabilized fibers.

We record the interference between the QKD lasers in Charlie on a fast photodiode (the traces are normalized between 0 and 1. a In an unstabilized condition the instantaneous phase drifts by 30 rad/ms and is folded back when it exceeds the [0: π] interval. b When the fiber is stabilized, the phase remains stable. In this measurement, the interferometer was stabilized far from the folding point, i.e., in a condition where phase fluctuations were directly mapped into intensity fluctuations, to investigate the residual noise processes. c The power spectral density of the phase. A significant reduction in the noise is observed in a stabilized condition (red) with respect to an unstabilized condition (blue). The apparent plateau observed at Fourier frequencies below 3 kHz in an unstabilized condition is an artifact originated by the folding of the interferometer response. At high Fourier frequency, similar noise is observed in the two traces, mainly due to the residual QKD lasers noise within the locking bandwidth, whose servo bumps are clearly observed around 900 kHz, and the self-delayed interference of the reference and sensing lasers, which give rise to the characteristic ripples pattern in the Fourier frequency range between 10 and 100 kHz (see Supplementary Information for a detailed analysis).