Point-to-point quantum privacy communication over a standard telecommunication fiber link can be implemented by continuous-variable quantum key distribution (CV QKD). However, as communication networks develop, the two-party CV QKD system may hardly meet the requirements of secret key sharing of multiple users (at least three users). In this paper, we consider a protocol called quantum secret sharing (QSS) which allows a legitimate user, a so-called dealer, to share a secret key with multiple remote users through an insecure quantum channel. These users can correctly recover the dealer's secret key only when they work cooperatively. We carry out QSS with discretely modulated coherent states (DMCSs) because they are easy to prepare and resilient to losses. An asymptotic security proof for the proposed DMCS-based QSS protocol against both eavesdroppers and dishonest users is presented. Numerical simulation based on a linear bosonic channel shows that the maximal transmission distance of the DMCS-based QSS protocol reaches more than 100 km, and it can be further lengthened by exploiting a higher-dimensional discrete modulation strategy. Moreover, the composable security of the DMCS-based QSS protocol is also presented.

中文翻译：

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使用离散调制相干态的量子秘密共享

可以通过连续可变量子密钥分发（CV QKD）来实现标准电信光纤链路上的点对点量子隐私通信。但是，随着通信网络的发展，两方CV QKD系统可能几乎无法满足多个用户（至少三个用户）共享密钥的要求。在本文中，我们考虑了一种称为量子秘密共享（QSS）的协议，该协议允许合法用户（所谓的经销商）通过不安全的量子通道与多个远程用户共享秘密密钥。这些用户只有在合作时才能正确恢复经销商的秘密密钥。我们执行具有离散调制相干态（DMCS）的QSS，因为它们易于准备并且可以抵抗损失。提出了针对窃听者和不诚实用户的基于DMCS的QSS协议的渐近安全性证明。基于线性玻色子信道的数值模拟表明，基于DMCS的QSS协议的最大传输距离超过100 km，并且可以通过使用更高维的离散调制策略来进一步延长。此外，还提出了基于DMCS的QSS协议的可组合安全性。