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Microsystems Electronics and Acoustics

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

Bohdan Bilash

Published Jul 6, 2020• 0 citations
Publisher

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.

DOI
10.20535/2523-4455.mea.201253

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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.
We present the Low Density Parity Check (LDPC) forward error correction algorithm adapted for the Quantum Key Distribution (QKD) protocol in a form readily applied by developers. A sparse parity check matrix is required for the LDPC algorithm and we suggest using some that have been defined by the IEEE and ETSI standards organizations for use in various communication protocols. We evaluate the QKD performance of these various parity check matrices as a function of the quantum bit error rate. We also discuss the computational precision required for this LPDC algorithm. As QKD evolves towards deployment, complete algorithm descriptions and performance analysis, as we present, will be required.
For the post-processing of the quantum-key-distribution (QKD) system, the error correction is the most important step, whose efficiency significantly influences the final key generation rate. Traditionally, the error-correction algorithm is developed based on the binary symmetrical channel model. However, this may not comply with the actual channel status. For example, for the fiber-based QKD system, differentiable statuses of the fiber (unstable or steady) should exist for some time and cause different bit error rates. If this channel feature can be exploited, it may considerably improve the error-correction efficiency. This paper proposes to introduce the Gilbert-Elliott (GE) model to analyze the QKD channel. The error-correction algorithm adopts the low-density parity-check (LDPC) code. The GE nodes are added into the traditional belief propagation (BP) algorithm of the LDPC decoder. Simulation results showed that the remaining frame error rate could be improved from ${10}^{\ensuremath{-}2}$ (or ${10}^{\ensuremath{-}3}$) to ${10}^{\ensuremath{-}4}$. An actual QKD system with the quantum channel state under manual control was adopted to collect the key bit string. By analyzing the occurrence probability of the kkk consecutive "1," the key bit string showed closely matched distribution with the GE model prediction. After the error correction, the remaining bit error rate of the modified BP algorithm was significantly smaller than that of the standard BP algorithm with an improvement of more than 2 orders of magnitude. Both simulation and actual experimental results demonstrate that our proposed method can greatly improve the error-correction efficiency if the channel characteristic of the QKD system is accurately exploited, which provides an efficient way to generate a higher key rate.
Quantum key distribution (QKD) is a promising technique to share unconditionally secure keys between remote parties. As an essential part of a practical QKD system, reconciliation is responsible for correcting the errors due to the quantum channel noise by exchanging information through a public classical channel. In the present work, we propose a novel syndrome-based low-density parity-check (LDPC) reconciliation protocol to reduce the information leakage of reconciliation by fully utilizing the syndrome information that was previously wasted. Both theoretical analysis and simulation results show that our protocol can evidently reduce the information leakage as well as the number of communication rounds.
Post-processing is a significant step in quantum key distribution (QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error reconciliation protocol, which can lead to an increase in the secure key generation rate, is one of the main performance indicators of QKD setups. In this paper, we propose a multi-low-density parity-check codes based reconciliation scheme, which can provide remarkable perspectives for highly efficient information reconciliation. By testing our approach through data simulation, we show that the proposed scheme combining multi-syndrome-based error rate estimation allows for a more accurate estimation of the error rate as compared with random sampling and single-syndrome estimation techniques before the error correction, as well as a significant increase in the efficiency of the procedure without compromising security and sacrificing reconciliation efficiency.
Secret keys can be established through the use of a Quantum channel monitored through classical channel which can be thought of as being error free. The quantum channel is subject to massive erasures and discards of erroneously measured bit values and as a result the error correction mechanism to be used must be accordingly modified. This paper addresses the impact of error correction (known as Reconciliation) on the secrecy of the retained bits and issues concerning the efficient software implementation of the Low Density Parity Check algorithm in the Quantum Key Distribution environment. The performance of three algorithmic variants are measured through implementations and the collected sample data suggest that the implementation details are particularly important