Quantum key distribution protocols can be based on quantum error correcting codes, where the structure of the code determines the post processing protocol applied to a raw key produced by BB84 or a similar scheme.  Luo and Devetak showed that basing a similar protocol on entanglement-assisted quantum error-correcting codes (EAQECCs) leads to quantum key expansion (QKE) protocols, where some amount of previously shared secret key is used as a seed in the post-processing stage to produce a larger secret key. One of the promising aspects of EAQECCs is that they can be constructed from classical linear codes that don't satisfy the dual-containing property, which among other things allows the use of low density parity-check (LDPC) codes with girth greater than 4, for which the iterative decoding algorithm has better performance.  We looked into QKE based on a family of EAQECCs generated by classical finite geometry (FG) LDPC codes.  Very efficient iterative decoders exist for these codes, and they were shown by Hsieh, Yen and Hau to produce quantum LDPC codes that require very little entanglement.  We modify the original QKE protocol to detect bad code blocks without the consumption of secret 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 net key production rate, but without increasing the consumption rate of pre-shared key.  Numerical simulations for the family of FG LDPC codes show that this improved QKE protocol has a good net key production rate even at relatively high error rates, for appropriate code choices.


Talk Number PIRSA:13040108
Speaker Profile Todd Brun
Collection Quantum Information