No-Go Theorem for Gaussian Quantum Repeaters from Fractional Extendibility
Solves an open problem in quantum communication by showing that Gaussian operations alone are insufficient to overcome photon loss, guiding future repeater designs toward non-Gaussian approaches.
This work proves that Gaussian quantum repeaters cannot enhance the quantum capacity of pure-loss channels beyond direct transmission, establishing a fundamental limitation for Gaussian repeater protocols.
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.