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We consider a quantum key expansion (QKE) protocol based onentanglement-assisted quantum error-correcting codes (EAQECCs). In theseprotocols, a seed of a previously shared secret key is used in thepost-processing stage of a standard quantum key distribution protocol like theBennett-Brassard 1984 protocol, in order to produce a larger secret key. Thisprotocol was proposed by Luo and Devetak, but codes leading to good performancehave not been investigated. We look into a family of EAQECCs generated byclassical finite geometry (FG) low-density parity-check (LDPC) codes, for whichvery efficient iterative decoders exist. A critical observation is that almostall errors in the resulting secret key result from uncorrectable block errorsthat can be detected by an additional syndrome check and an additional samplingstep. Bad blocks can then be discarded. We make some changes to the originalprotocol to avoid the consumption of the preshared key when the protocol fails.This allows us to greatly reduce the bit error rate of the key at the cost of aminor reduction in the key production rate, but without increasing theconsumption rate of the preshared key. We present numerical simulations for thefamily of FG LDPC codes, and show that this improved QKE protocol has a goodnet key production rate even at relatively high error rates, for appropriatechoices of these codes.

Family of Finite Geometry Low-Density Parity-Check Codes for Quantum Key Expansion