改进的低秩校验码多维解码算法提升CV-QKD效率与安全性

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本文主要探讨了连续变量量子密钥分发（Continuous-Variable Quantum Key Distribution, CV-QKD）系统中的关键环节——多维协调算法的改进策略。在CV-QKD中，多维协调是实现可靠密钥传输的重要步骤，它涉及到量子信号与经典信息的交互，以确保接收端能够纠正由于噪声和失真造成的误码，从而生成高纯度的共享密钥。传统多维协调通常依赖于编码器提供的规范信息来进行初始解码消息计算，这可能会增加系统的复杂性和资源消耗。为了优化这一过程，研究者提出了一个创新的方法，即针对低密度奇偶校验码（Low Density Parity Check Code, LDPC）设计了一种无需编码器规范信息的初始解码策略。这种方法的优势在于，它降低了协调过程中的通信流量和存储资源的需求，这对于提升系统效率、处理速度以及延长最大传输距离具有显著作用。理论分析部分深入探讨了新算法的工作原理及其对协调效率的影响。结果显示，尽管在去除了编码器规范信息的情况下进行操作，但改进后的算法仍能保持较高的协调效率，这意味着在保持性能稳定的同时实现了资源的有效节省。此外，通过减少经典信道认证所需的安全密钥消耗，该方案间接提高了安全密钥速率，这对于实现高速的CV-QKD系统至关重要。仿真结果进一步证实了这些理论预期，证明了改进算法在实际应用中的可行性和有效性。在实际的CV-QKD系统中，这种优化措施对于降低运行成本、提高整体性能和扩展系统范围具有重要的意义。因此，这项工作不仅为CV-QKD技术的未来发展提供了新的解决方案，也为其他量子通信协议的设计提供了一个有益的参考。本文提出的改进多维协调算法在量子信息处理领域（Quantum Information Processing）取得了突破，为提升CV-QKD系统的实用性、稳定性和安全性做出了重要贡献，具有重要的科研价值和实际应用潜力。

25 Page 4 of 20 Q. Li et al.

2 Preliminaries

2.1 Multidimensional reconciliation

The central idea of multidimensional reconciliation is reducing the reconciliation of

Gaussian variables to the channel coding on the BIAWGN channel through performing

a clever rotation on unit sphere S

d−1

of R

and then to correct the rotated data.

In multidimensional reconciliation scheme, Alice and Bob need ﬁrstly combine d

continuous-variable raw keys into a d-dimensional vector. We only discuss the recon-

ciliation of CV-QKD with Gaussian modulation in this paper. Let X = (x

, x

,...,x

)

and Y = (y

, y

,...,y

) corresponding to correlated Gaussian vectors of Alice and

Bob, respectively, then Y = X +Z with X ∼ N (0, V

)

, Z ∼ N (0,σ

)

in the direct

reconciliation case, and X = Y + Z



with Y ∼ N (0, V

+σ

)

, Z



∼ N (0,σ

2

)

the reverse reconciliation case, where V

is modulation variance and σ

, σ

2

are noise

variances. For long-distance CV-QKD protocols, the reverse reconciliation is required,

which takes Bob’s sequence as target keys to correct Alice’s, i.e., Bob is the encoder

and Alice is the decoder. The process of reverse multidimensional reconciliation is

described as follows:

(1) Alice and Bob normalize t heir Gaussian variables X and Y to x =

||X||

and

y =

||Y ||

, respectively, where ||X|| =





and ||Y || =





;

(2) Bob randomly generates a bit string (b

, b

,...,b

), b

∈{0, 1} corresponding

a random vector u =



(−1)

√

, ···,

(−1)

√



∈



−1/

√

d, 1/

√



with uniform

distribution on S

d−1

and computes a orthogonal transformation M(y, u) such

that M(y, u)y = u then sends the transformation M(y, u) to Alice over a public

classical authenticated channel;

(3) Alice operates the same orthogonal rotation M(y, u) on x to map the Gaussian

variables to v = M(y, u)x, which is a noisy version of u;

(4) Bob sends the norm information ||Y ||and some syndrome information S to Alice.

Then, Alice computes the initial iteration information m

= ln

(

u(0)|v

)

Pr(u(1)|v

)

, and uses

the classical error-correction algorithm to decode v to u, where the conditional

probability Pr

(

u(s)|v

)

is given by Eq. (1).

Pr(u(s)|v

) = Ke

−(||X ||v

−||Y ||u(s))

2σ



2πσ

, (1)

where s ∈{0, 1}, u(s) =

(−1)

√

, K is a normalization factor meeting Pr

(

u(0)|v

)

(

u(1)|v

)

= 1.

After Step 3, a virtual BIAWGN channel with binary input u and continuous-

variable output v has been constructed. Then, the Gaussian variables reconciliation

problem has been transformed into error-correction problem on the BIAWGN channel.

In order to obtain the same key vector u as Bob, Alice needs to decode v by using the

classic error-correction algorithm in Step 4.

123

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