Family of finite geometry low-density parity-check codes for quantum key expansion

摘要

We consider a quantum key expansion (QKE) protocol based on entanglement-assisted quantum errorcorrectingncodes (EAQECCs). In these protocols, a seed of a previously shared secret key is used in thenpostprocessing stage of a standard quantum key distribution protocol like the Bennett-Brassard 1984 protocol,nin order to produce a larger secret key. This protocol was proposed by Luo and Devetak, but codes leadingnto good performance have not been investigated. We look into a family of EAQECCs generated by classicalnfinite geometry (FG) low-density parity-check (LDPC) codes, for which very efficient iterative decoders exist.nA critical observation is that almost all errors in the resulting secret key result from uncorrectable block errorsnthat can be detected by an additional syndrome check and an additional sampling step. Bad blocks can then bendiscarded. We make some changes to the original protocol to avoid the consumption of the preshared key whennthe protocol fails. This allows us to greatly reduce the bit error rate of the key at the cost of a minor reduction innthe key production rate, but without increasing the consumption rate of the preshared key. We present numericalnsimulations for the family of FG LDPC codes, and show that this improved QKE protocol has a good net keynproduction rate even at relatively high error rates, for appropriate choices of these codes.