Optimal Low Density Parity Check Matrices to Correct Quantum Key Errors for QKD

In this paper, the parity-check matrices that can be used in low density parity check (LDPC) based error correction method for quantum key distribution are analyzed. The quantum key distribution system has inevitable errors in sifted key that must be corrected by an error correction algorithm to create a secure key. In this analysis, 1000-bit sifted keys are divided into 50 parts. The algorithm creates 50 syndromes corresponding to each part by multiplying 10 × 20 bit parity-check matrices. The algorithm sends the generated syndrome to the other side, which also divides the sifted key into 50 parts, creates a syndrome from each part, and compares with the received syndrome. If the syndromes are different, these sifted key parts are discarded. However, there may be situations where different parts may have the same syndromes. Therefore, it is necessary to find such an optimal matrix that removes the probability of getting the same syndromes at different parts of the sifted key