Reverse Reconciliation for Optimal Error Correction in Quantum Key Distribution

In this work, we introduce a new method for the establishment of a symmetric secret key through the reconciliation process in QKD systems that, we claim, is immune to the error rate of the quantum channel and, therefore, has an efficiency of 100% since it does not present losses during the distillation of secret keys. Furthermore, the secret rate is scaled to the square of the number of pulses on the destination side. The method only requires a single data exchange from Bob over the classic channel. We affirmed that our results constitute a milestone in the field of QKD and error correction methods at a crucial moment in the development of classical and quantum cryptanalytic algorithms. We believe that the properties of our method can be evaluated directly since it does not require the use of complex formal-theoretical techniques. For this purpose, we provide a detailed description of the reconciliation algorithm. The strength of the method against PNS and IR attacks is discussed. Furthermore, we define a method to analyze the security of the reconciliation approach based on frames that are binary arrays of 2x2. As a result, we came to the conclusion that the conjugate approach can no longer be considered secure, while we came up with a way to increase the secret gain of the method with measured bits.