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- Quantum key expansion based on entanglement-assisted quantum LDPC codes

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.

Event Type:

Seminar

Collection/Series:

Scientific Area(s):

Speaker(s):

Event Date:

Wednesday, April 3, 2013 - 16:00 to 17:30

Location:

Space Room

©2012 Perimeter Institute for Theoretical Physics