![]() In this work, we generalize the error-correction code to the scenario with general correlated and heterogeneous Gaussian noises, including memory effects. Enabled by Gottesman-Kitaev-Preskill states as ancilla, the code overcomes the no-go theorem of Gaussian error correction. proposed an error-correction code to maintain the infinite-dimensional-Hilbert-space nature of bosonic systems by encoding a single bosonic mode into multiple bosonic modes. While most efforts aim at protecting qubits encoded into the infinite-dimensional Hilbert space of a bosonic mode, Ref. As bosonic quantum systems play a role in quantum sensing, communication, and computation, it is useful to design error-correction codes suitable for these systems against various different types of noises. Quantum error correction is essential for robust quantum-information processing with noisy devices. This code allows the system to maintain a high key extraction rate under various SNRs, paving the way for practical applications of CV-QKD systems with different transmission distances. Simulation results show that we can achieve more than 98% reconciliation efficiency in a range of code rate variation using only one RL-LDPC code that can support high-speed decoding with an SNR less than −16.45 dB. We design the RL-LDPC matrix with a code rate of 0.02 and easily and effectively adjust this rate from 0.016 to 0.034. Moreover, this technique can significantly reduce the cost of constructing a new matrix. Thus, we introduce Raptor-like LDPC (RL-LDPC) codes into the CV-QKD system, exhibiting both the rate compatible property of the Raptor code and capacity-approaching performance of MET-LDPC codes. However, the process of designing a low-rate MET-LDPC code with good performance is extremely complicated. Multi-edge type low-density parity-check (MET-LDPC) codes are suitable for CV-QKD systems because of their Shannon-limit-approaching performance at a low signal-to-noise ratio (SNR). In the practical continuous-variable quantum key distribution (CV-QKD) system, the postprocessing process, particularly the error correction part, significantly impacts the system performance.
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