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

TL;DR

This paper explores a quantum key expansion protocol using finite geometry LDPC codes, improving key rate and error detection without increasing pre-shared key consumption, through enhanced decoding and error handling methods.

Contribution

It introduces a novel quantum key expansion protocol leveraging finite geometry LDPC codes with efficient decoding, reducing key errors without extra pre-shared key consumption.

Findings

Effective error detection via syndrome checks and sampling.

Reduced bit error rate with minimal key rate impact.

Good net key production at higher error rates.

Abstract

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