Fig. 4: Phase fluctuations over time.
From: Coherent phase transfer for real-world twin-field quantum key distribution
a The deviation of the phase σφ between the two QKD lasers interfering in Charlie at different timescales, in an unstabilized (blue) and stabilized (red) condition. For this calculation, we acquired the interference pattern over 4 s and subdivided it into shorter time frames, calculating σφ for each frame. The shadowed areas indicate upper thresholds for relevant values of the QBER. The phase and corresponding QBER were retrieved from the interference pattern according to the procedures described in the “Methods”. The arrows indicate timescales where the QKD lasers noise and the uncompensated fiber noise (differential fluctuations at the two wavelengths) become relevant. For a given TF-QKD implementation, the quantum states transmission (QS) must be interleaved with realignment frames encoding a reference phase (ref.) after a time Tal. This allows detection and stabilization of the interferometer noise δ, and ensures that a specified QBER is not exceeded: in our case, to preserve a QBER < 1%, Tal amounts to 100 μs and 0.1 s using an unstabilised or stabilized interferometer respectively. While in the former case realignment frames are absolutely required (b), in the latter case it becomes possible to exploit variations in the QBER itself to derive information about the interferometer phase noise and stabilise it. Even in the worst case scenario in which this is not possible because of a too high fiber loss, realignment frames need to be applied at a much slower rate (c), effectively enabling duty cycles higher than 90% (see Supplementary Information).
