Photon loss in optical channels fundamentally limits long-range reliable quantum communication. A standard approach to overcoming this limitation is the use of quantum repeater nodes, which typically perform experimentally demanding non-Gaussian operations. However, whether Gaussian repeater protocols can enhance quantum communication rates over bosonic attenuation channels has remained open. In this work, we prove a no-go theorem for Gaussian quantum repeaters in a quantum network. Specifically, we show that any repeater chain composed of Gaussian operations, homodyne measurements, and arbitrary classical communication cannot enhance the quantum capacity of a pure-loss attenuation channel beyond that achievable by direct transmission. Our proof introduces a generalisation of $k$-extendibility to a notion of fractional extendibility for Gaussian states and establishes some of its useful properties, thereby providing a powerful framework for analysing Gaussian quantum networks.

翻译：光纤信道中的光子损耗从根本上限制了远距离可靠量子通信。克服这一局限的标准方法是使用量子中继节点，而这些节点通常需要执行实验上要求极高的非高斯操作。然而，高斯中继协议能否提高玻色子衰减信道中的量子通信速率至今仍是悬而未决的问题。在本研究中，我们证明了量子网络中高斯量子中继器的禁戒定理。具体而言，我们表明任何由高斯操作、零差测量和任意经典通信组成的中继链，都无法使纯损耗衰减信道的量子容量超过直接传输所能达到的极限。我们的证明将$k$-可扩展性推广为高斯态的分数可扩展性概念，并建立了该概念的一些有用性质，从而为分析高斯量子网络提供了一个强有力的框架。