No-Go Theorem for Gaussian Quantum Repeaters from Fractional Extendibility
2026-06-03 • Information Theory
Information Theory
AI summaryⓘ
The authors studied a kind of quantum communication method using light signals that get weaker over long distances. They looked at whether using only certain simple operations called Gaussian operations at repeater points could improve the rate of communication. They found that these Gaussian repeaters cannot do better than sending the signals directly without any repeaters. To prove this, the authors developed a new concept called fractional extendibility for Gaussian states, which helps analyze such quantum networks.
quantum communicationphoton lossquantum repeaterGaussian operationsbosonic channelsquantum capacityhomodyne measurementk-extendibilityfractional extendibilitypure-loss channel
Authors
Rabsan Galib Ahmed, Graeme Smith
Abstract
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.