Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates.

中文翻译：

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离散调制连续变量量子密钥分配的渐近安全性分析

具有离散调制功能的连续变量量子密钥分发（CV QKD）协议由于其实验简单性以及在量子安全网络中大规模部署的巨大潜力而​​引起人们的关注，但其安全性分析不如高斯调制方案先进。在这项工作中，我们采用一种数值方法来分析离散调制协议在渐近极限下抵抗集体攻击的安全性，从而为具有有限大小效应的完整安全性证明铺平了道路。虽然我们的方法通常适用于离散调制方案，但我们将重点放在具有四级调制的CV QKD协议的两个变体上。有趣的是，由于我们证明方法的严格性，我们表明，与先前的二进制和三元调制方案的安全性证明相比，该协议能够在实验上可行的参数下，在更长的距离上实现更高的密钥速率，并且还能产生与高斯调制方案相当的密钥速率。此外，由于我们的安全性分析方法用途广泛，因此它使我们能够评估离散调制协议的变体，包括直接和反向对帐以及后选择策略。特别是，我们证明了与反向对帐相结合的数据后选择可以提高关键率。它使我们能够评估离散调制协议的变体，包括直接和反向对帐以及后选择策略。特别是，我们证明了与反向对帐相结合的数据后选择可以提高关键率。它使我们能够评估离散调制协议的变体，包括直接和反向对帐以及后选择策略。特别是，我们证明了与反向对帐相结合的数据后选择可以提高关键率。