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AIP conference proceedings

Adaptive algorithms of error correction and error estimation in quantum cryptography

Asel Sagingalieva, Dmitry Anatolevich Kronberg

Published Jan 1, 2021• 1 citation
Publisher

Abstract

Quantum cryptography provides methods for secret key distribution between the two distant users. An important step in quantum key distribution protocols is the correction of errors that occur during the transmission and implementation of the protocol. Here we consider error estimation and error correction with linear codes such as repetition code, Hamming code, low density parity check (LDPC) code. The paper investigates the increase in the efficiency of error correction using a combination of a repetition code and a LDPC code for a high error probability.

DOI
10.1063/5.0055360

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Quantum cryptography provides methods for secret key distribution between the two distant users. An important step in quantum key distribution protocols is the correction of errors that occur during the transmission and implementation of the protocol. Here we consider error estimation and error correction with linear codes such as repetition code, Hamming code, low density parity check (LDPC) code. The paper investigates the increase in the efficiency of error correction using a combination of a repetition code and a LDPC code for a high error probability.
Error correction is a crucial stage in quantum key distribution (QKD) protocols—a promising field of modern cryptography where the secrecy of the shared key information is guaranteed by the laws of quantum mechanics. Currently, there are many effective approaches to error correction in QKD. However, most of them, due to their generic nature, fail to leverage the specific features of particular protocol implementations. This work demonstrates that accounting for the hardware specifics of a QKD system implementing the time-bin protocol enables a significant increase in error correction performance. For the considered QKD system, we have experimentally obtained estimates of the Quantum Bit Error Rate (QBER) observed for each combination of bit and detector. The differences in the obtained estimates reveal that the quantum channel can be modeled as a non-uniform binary channel. Furthermore, based on computational experiments with a model of the quantum channel, it was established that adapting the error correction procedure to its properties can achieve up to a 2.7-fold reduction in the LDPC code decoding failure rate at low error levels.
The authors consider error correction in quantum key distribution. To avoid that Alice and Bob unwittingly end up with different keys, precautions must be taken. Before running the error correction protocol, Bob and Alice normally sacrifice some bits to estimate the error rate. To reduce the probability that they end up with different keys to an acceptable level, the authors show that a large number of bits must be sacrificed. Instead, if Alice and Bob can make a good guess about the error rate before the error correction, they can verify that their keys are similar after the error correction protocol. In this study, the authors show that this verification can be done by utilising properties of low‐density parity check codes used in the error correction. The authors compare the different methods and show that by verification it is often possible to sacrifice less bits without compromising security. The improvement is heavily dependent on the error rate and the block length, but for a key produced by the IdQuantique system Clavis 2 , the increase in the key rate is ∼5%. The authors also show that for systems with large fluctuations in the error rate, a combination of the two methods is optimal.
We consider error correction in quantum key distribu-tion. To avoid that Alice and Bob unwittingly end up with different keys precautions must be taken. Before running the error correction protocol, Bob and Al-ice normally sacrifice some bits to estimate the error rate. To reduce the probability that they end up with different keys to an acceptable level, we show that a large number of bits must be sacrificed. Instead, if Alice and Bob can make a good guess about the er-ror rate before the error correction, they can verify that their keys are similar after the error correction protocol. This verification can be done by utilizing properties of Low Density Parity Check codes used in the error correction. We compare the methods and show that by verification it is often possible to sac-rifice less bits without compromising security. The improvement is heavily dependent on the error rate and the block length, but for a key produced by the IdQuantique system Clavis2, the increase in the key rate is approximately 5 percent. We also show that for systems with large fluctuations in the error rate a combination of the two methods is optimal.
The purpose of reconciliation, one of classical aspects of quantum key distribution (QKD) protocol, is to mitigate errors after the distribution of quantum information over a quantum channel. In this paper, a rate-adaptive method is proposed by means of a channel coding scheme where specific low-density parity-check (LDPC) codes are adapted in the Slepian-Wolf coding system. Puncturing and shortening techniques are adopted to optimize their coding rates with all possible cases of error in QKD. This successful method utilizes the knowledge of the quantum bit error rate (QBER) based on the maximum-likelihood estimator with respect to the syndrome information. Its benefit is that avoids wasting sample keys in the traditional channel estimation and thus increases the size of the final secret key. Evidently, simulation results confirm an improvement in the reconciliation efficiency with minimal interaction that suitable for high QKD throughput applications.
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
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.