Optimal Low Density Parity Check Matrices to Correct Quantum Key Errors for QKD

Bohdan Olehovych Bilash

doi:10.20535/2523-4455.mea.201253

Abstract

In this paper, the parity-check matrices that can be used in low density parity check (LDPC) based error correction method for quantum key distribution are analyzed. The quantum key distribution system has inevitable errors in sifted key that must be corrected by an error correction algorithm to create a secure key. In this analysis, 1000-bit sifted keys are divided into 50 parts. The algorithm creates 50 syndromes corresponding to each part by multiplying 10 × 20 bit parity-check matrices. The algorithm sends the generated syndrome to the other side, which also divides the sifted key into 50 parts, creates a syndrome from each part, and compares with the received syndrome. If the syndromes are different, these sifted key parts are discarded. However, there may be situations where different parts may have the same syndromes. Therefore, it is necessary to find such an optimal matrix that removes the probability of getting the same syndromes at different parts of the sifted key.

Highlights

Quantum key distribution (QKD) is a system that can securely share an identical key between two distant parties, Alice and Bob [1]
There are some subjects for research works on the QKD such as chip-scale system [4], long-distance communication [5], high secure key rate QKD [6]–[8], and efficient post-processing [9]
We have two messages: the original message, which is the sifted key of Alice, X, and changed to a certain number of bits equal to quantum bit error rate (QBER), the message that is the sifted key of Bob, Y

Summary

Introduction

At the error correction step, Alice and Bob have sifted keys, but they are slightly different from each other due to the background noises of the QKD system. We are sure that when error correction step, Eve will not know the information about the original bits between Alice and Bob. The other side decodes the syndrome and compares the results with its own. It is necessary to come up with such a method of correcting the errors in Alice and Bob's sifted keys so that Eve cannot find out about them.

Results

Conclusion