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arXiv:2305.08631 · International Symposium on Turbo Codes and Iterative Information Processing

Information Reconciliation for High-Dimensional Quantum Key Distribution using Nonbinary LDPC codes

Ronny Müller, Davide Bacco, Leif Katsuo Oxenløwe, Søren O. Forchhammer

Published Sep 4, 2023• 2 citations
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Abstract

Information Reconciliation is an essential part of Quantum Key distribution protocols that closely resembles Slepian-Wolf coding. The application of nonbinary LDPC codes in the Information Reconciliation stage of a high-dimensional discrete-variable Quantum Key Distribution setup is proposed. We model the quantum channel using a q-ary symmetric channel over which qudits are sent. Node degree distributions optimized via density evolution for the Quantum Key Distribution setting are presented, and we show that codes constructed using these distributions allow for efficient reconciliation of large-alphabet keys.

DOI
10.1109/istc57237.2023.10273570

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Information Reconciliation is an essential part of Quantum Key distribution protocols that closely resembles Slepian-Wolf coding. The application of nonbinary LDPC codes in the Information Reconciliation stage of a high-dimensional discrete-variable Quantum Key Distribution setup is proposed. We model the quantum channel using a q-ary symmetric channel over which qudits are sent. Node degree distributions optimized via density evolution for the Quantum Key Distribution setting are presented, and we show that codes constructed using these distributions allow for efficient reconciliation of large-alphabet keys.
We study the information reconciliation (IR) scheme for quantum key distribution (QKD) protocols. The IR for the QKD can be seen as the asymmetric Slepian-Wolf problem, which low-density parity-check (LDPC) codes can solve with efficient algorithms, i.e., the belief propagation. However, the LDPC codes are needed to be chosen properly from a collection of codes optimized for multiple key rates, which leads to complex decoder devices and performance degradation for unoptimized key rates. Therefore, it is desired that establish an IR scheme with a single LDPC code which supports multiple rates. To this end, in this paper, we propose an IR scheme with a rate-compatible non-binary LDPC code. Numerical results show the proposed scheme achieves IR efficiency comparable to the best know conventional IR scheme with lower decoding error rates.
Reconciliation is an essential part of any secret-key agreement protocol and hence of a quantum key distribution (QKD) protocol, where two legitimate parties are given correlated data and want to agree on a common string in the presence of an adversary, while revealing a minimum amount of information. In this paper, we show that for discrete-variable QKD protocols, this problem can be advantageously solved with low density parity check (LDPC) codes optimized for the binary symmetric channel (BSC). In particular, we demonstrate that our method leads to a significant improvement of the achievable secret key rate, with respect to earlier interactive reconciliation methods used in QKD.
Abstract In Quantum Key Distribution (QKD), two users extract a shared secret key using a quantum communication channel in the presence of an eavesdropper. Among QKD protocols, the ones based on Energy-Time (ET) entanglement of photons have been studied extensively due to their ability to generate high key rates from the arrival times of entangled photons. For the information reconciliation (IR) stage of ET-QKD protocols (where the users communicate using a classical channel in order to reconcile differences in their data), a scheme called multi-level coding (MLC) was proposed by Zhou et al. in prior work. The MLC scheme splits the raw key symbols into bit layers and utilizes binary Low-Density Parity-Check (LDPC) codes to encode each layer. Although binary LDPC codes are able to offer low complexity decoding for IR, they have poor error-correcting performance compared to their non-binary counterparts, thus leading to low key rates. Additionally, existing LDPC codes do not fully utilize the properties of the QKD channel to optimize the key rates. In this paper, we mitigate the above issues by proposing a flexible protocol for IR in ET-QKD systems called Non-Binary Multi-Level Coding NB-MLC(a) which is parameterized by a positive integer a. The NB-MLC(a) protocol is a generalization of the MLC scheme and utilizes NB-LDPC codes from a Galois field of size 2^a. We show that by using a small value of a, the NB-MLC(a) protocol significantly improves the key rate without much increase in complexity. To further improve the key rates of the NB-MLC(a) protocol, we propose i) a joint rate and degree distribution optimization (JRDO) algorithm to design the NB-LDPC codes for the protocol; ii) an interleaved decoding and communication (IDC) scheme to decode the different layers of the NB-MLC(a) protocol. The JRDO algorithm is designed to use the QKD channel information and we show that it results in a higher key rate than codes used in prior work. Additionally, the IDC scheme improves the key rate compared to the decoding and communication methods utilized previously in literature. Overall, the NB-MLC(a) protocol that uses JRDO LDPC codes and the IDC scheme results in a significant 40 − 60% improvement in key rates compared to prior work for ET-QKD systems.
Abstract Quantum key distribution (QKD) is the most mature application of quantum information technology. Information reconciliation is a crucial step in QKD and significantly affects the final secret key rates shared between two legitimate parties. We analyze and compare various construction methods of low-density parity-check (LDPC) codes and design high-performance irregular LDPC codes with a block length of 10 6 . Starting from these good codes and exploiting the slice reconciliation technique based on multilevel coding and multistage decoding, we realize high-efficiency Gaussian key reconciliation with efficiency higher than 95% for signal-to-noise ratios above 1. Our demonstrated method can be readily applied in continuous variable QKD.