Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction algorithm) frameworks - quantum key distribution based on systematic polar coding. This results in obtaining key rates greater than standard quantum key distribution (BB84) and its efficient version (eBB84) when finite-size regime and lower-error-rate quantum channel are considered.
Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction algorithm) frameworks - quantum key distribution based on systematic polar coding. This results in obtaining key rates greater than standard quantum key distribution (BB84) and its efficient version (eBB84) when finite-size regime and lower-error-rate quantum channel are considered.
Quantum Key Distribution (QKD) enables two parties to establish a common secret key that is information-theoretically secure by transmitting random bits that are encoded as qubits and sent over a quantum channel, followed by classical information processing steps known as information reconciliation and key extraction. Transmission of information over a quantum channel introduces errors that are generally considered to be due to the adversary's tempering with the quantum channel and needs to be corrected using classical communication over an (authenticated) public channel. Commonly used error-correcting codes in the context of QKD include cascade codes, low-density parity check (LDPC) codes, and more recently polar codes. In this work, we explore the applicability of designing of a polar code encoder based on a channel reliability sequence. We show that the reliability sequence can be derived and used to design an encoder independent of the choice of decoder. We then implement our design and evaluate its performance against previous implementations of polar code encoders for QKD as well as other typical error-correcting codes. A key advantage of our approach is the modular design which decouples the encoder and decoder design and allows independent optimization of each. Our work leads to more versatile polar code-based error reconciliation in QKD systems that would result in deployment in a broader range of scenarios.
Continuous-variable quantum key distribution faces significant challenges, including quantum channel instability, particularly fluctuations in the signal-to-noise ratio (SNR) and extremely low SNR scenarios. Furthermore, non-ideal polar codes, characterized by insufficient polarization in finite-length regimes, can lead to some sub-channels being neither completely noise-free nor fully noise-dominated. This phenomenon limits the error correction capability when such codes are applied to information reconciliation. To address these challenges, we propose a novel RC-LDPC-Polar code for the CV-QKD reconciliation algorithm. We combine the error resilience of LDPC codes with the efficiency advantages of polar coding. This scheme supports adaptive rate adjustment across varying SNR conditions. Our simulation experiments demonstrate that the RC-LDPC-Polar concatenated coding scheme achieves a lower error rate under varying SNR conditions. Meanwhile, the proposed scheme achieves a higher final key rate and a longer transmission distance.
Post-processing in BB84-based Quantum Key Distribution (QKD) must simultaneously ensure error correction, preserve secrecy, and satisfy strict resource constraints on embedded or edge devices. These competing requirements make the choice of coding strategy a system-level co-design problem involving both communication performance and decoder implementation cost. In this work, we present a comparative co-design framework that selects among LDPC, Polar, BCH, and Hamming codes based on real-time estimates of the quantum bit error rate (QBER), desired burn rate, and available decoding resources. We evaluate coding on the quantum channel and on the classical side-channel, quantifying their impact on residual BER, entropy loss, computational complexity, and secret-key rate. The resulting operational boundaries identify which codes are optimal in low-, moderate-, and high-error regimes. These boundaries provide a practical approach for implementing efficient BB84 reconciliation in embedded and edge QKD systems.
Combined with one-time pad encryption scheme, quantum key distribution guarantees the unconditional security of communication in theory. However, error correction and privacy amplification in the post-processing phase of quantum key distribution result in high time delay, which limits the final secret key generation rate and the practicability of quantum key distribution systems. To alleviate this limitation, this paper proposes an efficient post-processing algorithm based on polar codes for quantum key distribution. In this algorithm, by analyzing the channel capacity of the main channel and the wiretap channel respectively under the Wyner's wiretap channel model, we design a codeword structure of polar codes, so that the error correction and privacy amplification could be completed synchronously in a single step. Through combining error correction and privacy amplification into one single step, this efficient post-processing algorithm reduces complexity of the system and lower the post-processing delay. Besides, the reliable and secure communicaiton conditions for this algorithm has been given in this paper. Simulation results show that this post-processing algorithm satisfies the reliable and secure communication conditions well.
With the rapid improvement of quantum computing technology, quantum key distribution(QKD) is a hot technology. Information reconciliation is a key step of QKD which is useful for correcting key error. Classical message interaction is necessary in a practical information reconciliation scheme, which makes the efficiency of these protocols decreased. Therefore, some one-way information reconciliation schemes based on low-density parity-check(LDPC) codes and polar codes are proposed. Here we propose a concatenated method of IR schemes which can achieve any given error rate level without the need of interactions. Compared with the one-way IR schems based on LDPC codes and polar codes, the IR schemes based on the proposed concatenated method can get lower bit error rates after error correction, which can also reduce the communication delay and system complexity of QKD, improve the final key generation rate and enhance the practicability of QKD system.
Quantum key distribution is considered as one of the safe ways of distributing keys among the frames employed in communication. In 1984, BB84 appeared first as a protocol for QKD. In the present study paper, we proposed a new way of encoding a stream of bits into polarized photons using Legendre Symbol (a/p), where both of the sender and the receiver negotiate of using the function of Legendre symbol. Hence, in this case the proposed protocol uses only quantum channel instead of the classical channel, this leads to less time spent and less quantum error rate occurring comparing with the previous BB84 protocol. The experimental outcome confirms that the proposed protocol delivers efficient results comparing with the original BB84 protocol.