Improved Data Post-Processing in Quantum Key Distribution and Application to Loss Thresholds in device independent QKD

Security proofs of quantum key distribution (QKD) often require post-processing schemes to simplify the data structure, and hence the security proof. We show a generic method to improve resulting secure key rates by partially reversing the simplifying post-processing for error correction purposes. We apply our method to the security analysis of device-independent QKD schemes and of detection-device-independent QKD schemes, where in both cases one is typically required to assign binary values even to lost signals. In the device-independent case, the loss tolerance threshold is cut down by our method from 92.4% to 90.9%. The lowest tolerable transmittance of the detection-device-independent scheme can be improved from 78.0% to 65.9%