High-Dimensional Reconciliation Algorithm For Continuous Variable Quantum Key Distribution

Quantum key distribution combined with "one-time pad " can realize the information theory security quantum secure communication defined by Shannon,the security of which is not affected by computing power and can provide technical guarantee for the safe transmission of information.Continuous variable quantum key distribution has the advantages of easy compatibility with classical optical communication systems and high key generation rate,which has attracted the attention of many researchers.The legitimate communication parties can obtain a set of relevant original key data based on the quantum Non-Cloning Theorem and Uncertainty Principle and other basic quantum physics principles in the physical part.However,due to the noise effect of quantum channel and the interference of potential eavesdropper,the original key data is inconsistent and eavesdropper may obtain part of the key information.In order to extract the consistent and secure key,it is necessary to correct the errors of information and compress the raw key through classical post-processing to obtain the unconditionally secure final key.Due to the weak quantum signal itself,the signal-to-noise ratio of the original key data after transmission through the channel is very low,thus contributes to the extremely high difficulty and complexity of error correction.Therefore,the information reconciliation stage in classical post-processing is one of the main technical bottlenecks limiting the performance of continuous variable quantum key distribution.First of all,since the original key data is a continuous variable,the channel encoding and decoding technology cannot be directly implemented,so the data must be quantified first.However,the current data quantization method has the problem of high complexity or low quantization efficiency,so it can only obtain good quantization performance in some specific application scenarios.Secondly,due to the extremely low signal-to-noise ratio of the original key data and the extremely high difficulty of error correction,decoding algorithm with high computational complexity,high iteration times and long error correction code length should be adopted in error correction.The implementation complexity is high,which seriously affects the high-speed real-time key data processing.The above two key technical problems have an important impact on the security key rate of the continuous variable quantum key distribution system.In order to improve the reconciliation efficiency and reduce the decoding complexity,this paper proposes a high-dimensional reconciliation algorithm balancing both quantization efficiency and low quantization complexity,and a minimum sum decoding algorithm with high reconciliation efficiency and low decoding complexity based on deep neural network.The main work is as follows:1.A high-dimensional reconciliation algorithm based on Householder transform is proposed.The algorithm is based on the rotation mapping transformation of spherical code,and the quantization process is realized by any dimension mapping the continuous variables subject to Gaussian distribution into uniformly distributed binary bits on the unit sphere.Compared with the multidimensional reconciliation algorithm,it can significantly improve the quantization efficiency when signal-to-noise ratio is greater than 0.505,and greatly reduce the quantization complexity compared with the Slice reconciliation algorithm.The core principle of this algorithm is based on Householder transform,which is not restricted by the octonions in multidimensional reconciliation,so it can realize the quantization process infinitely close to Shannon limit within the range of its applicable signal-to-noise ratio,and maximize the quantization efficiency.The simulation results show that when the signal-to-noise ratio is 0.305,the quantization efficiency can reach more than 99%when performing 64dimensional negotiation.When the signal-to-noise ratio is 0.505,the quantification efficiency can reach more than 98%,which is about 4%higher than multi-dimensional negotiation.When signal-to-noise ratio is 0.4268,the reconciliation efficiency of 64-dimensional can exceed 97%,which is about 3%higher than that of 8-dimensional reconciliation.2.Proposed a high reconciliation efficiency and low decoding complexity error correction algorithm based on deep neural network.The algorithm simulates the decoding process of low-density parity check codes by constructing deep neural networks,and optimizes the network structure through continuous training and learning.The error correction performance of minimum sum decoding algorithm with low complexity but poor error correction performance can be improved to the same level as that of belief propagation decoding algorithm with high complexity and superior error correction performance.And it can realize efficient error correction when the length of the error correction code is short and the number of iterations is small.This algorithm converts a large number of multiplication and division operations in the traditional decoding algorithm into addition operations and greatly reduces the computational complexity.At the same time,the design and implementation of short code and low iteration times greatly reduce the storage requirements.These two points provide technical support for porting it to hardware platform to realize high-speed error correction,so that the real-time security key rate of continuous variable quantum key distribution can be greatly improved.The simulation results show that compared with the belief propagation decoding algorithm,the minimum decoding algorithm based on deep neural network can reduce the implementation complexity of the error correction process and maintain high reconciliation efficiency.