No-Go Theorem for Gaussian Quantum Repeaters from Fractional Extendibility

• URL: http://arxiv.org/abs/2606.05097v1
• Date: Wed, 03 Jun 2026 17:00:00 GMT
• Title: No-Go Theorem for Gaussian Quantum Repeaters from Fractional Extendibility
• Abstract summary: We prove a no-go theorem for Gaussian quantum repeaters in a quantum network.<n>Our proof introduces a generalisation of $k$-extendibility to a notion of fractional extendibility for Gaussian states.
• Score: 2.277447144331876
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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