No-Go Theorem for Gaussian Quantum Repeaters from Fractional Extendibility

2026-06-03

AI Summary

This work addresses the long-standing open question of whether Gaussian quantum repeaters can enhance the quantum communication rate over pure-loss bosonic channels. Introducing the concept of “fractional extendibility,” which generalizes the conventional notion of k-extendibility, the paper establishes a novel framework for analyzing Gaussian quantum networks. By leveraging Gaussian quantum information theory, channel capacity calculations, and modeling of repeater protocols, the authors rigorously prove that any repeater scheme composed solely of Gaussian operations, homodyne measurements, and classical communication cannot surpass the quantum capacity of direct transmission over a pure-loss channel. This result definitively clarifies the fundamental limitations of Gaussian repeaters in quantum communication.

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.

Problem

• Gaussian quantum repeaters
• quantum communication
• bosonic attenuation channels
• quantum capacity
• no-go theorem

Innovation

• Gaussian quantum repeaters
• no-go theorem
• fractional extendibility
• quantum capacity
• bosonic attenuation channels