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arxiv: 2606.05097 · v2 · pith:MNFBPJYHnew · submitted 2026-06-03 · 🪐 quant-ph · cs.IT· math.IT

No-Go Theorem for Gaussian Quantum Repeaters from Fractional Extendibility

Rabsan Galib Ahmed , Graeme Smith This is my paper

Pith reviewed 2026-07-01 07:31 UTC · model grok-4.3

classification 🪐 quant-ph cs.ITmath.IT
keywords Gaussian quantum repeatersno-go theoremfractional extendibilityquantum capacitypure-loss channelbosonic attenuationhomodyne detection
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The pith

Gaussian repeater chains using only Gaussian operations and homodyne measurements cannot enhance the quantum capacity of pure-loss channels beyond direct transmission.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper proves a no-go theorem showing that repeater protocols limited to Gaussian operations, homodyne measurements, and classical communication fail to increase the quantum capacity of pure-loss attenuation channels above the direct transmission limit. The result is significant because it demonstrates that experimentally simpler Gaussian-based repeaters are insufficient for improving long-range quantum communication rates over lossy optical channels. To achieve enhancement, repeater nodes must incorporate non-Gaussian operations. The authors develop a new framework of fractional extendibility for Gaussian states to establish this bound.

Core claim

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. The proof relies on generalizing k-extendibility to fractional extendibility for Gaussian states and establishing its properties for analyzing Gaussian quantum networks.

What carries the argument

Fractional extendibility, a generalization of k-extendibility tailored to Gaussian states, used to bound the performance of Gaussian quantum networks.

If this is right

  • Repeater chains restricted to Gaussian operations and homodyne detection provide no advantage over direct transmission for pure-loss channels.
  • The quantum capacity remains the same as the no-repeater case.
  • Arbitrary classical communication between nodes does not help overcome this limitation.
  • This no-go applies specifically to the pure-loss bosonic channel.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Experimental efforts should prioritize developing non-Gaussian quantum operations for repeater nodes.
  • The fractional extendibility concept might extend to analyzing capacities in other continuous-variable systems.
  • Similar no-go theorems could apply to Gaussian-limited protocols in quantum key distribution or other communication tasks.

Load-bearing premise

The repeater nodes perform only Gaussian operations and homodyne measurements rather than arbitrary quantum operations.

What would settle it

An explicit construction of a Gaussian repeater protocol that achieves a strictly higher quantum capacity than direct transmission over a pure-loss channel.

Figures

Figures reproduced from arXiv: 2606.05097 by Graeme Smith, Rabsan Galib Ahmed.

Figure 1
Figure 1. Figure 1: FIG. 1. Choi state of the repeater chain, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Each repeater node prepares a bipartite state locally [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript proves a no-go theorem showing that repeater chains restricted to Gaussian operations, homodyne measurements, and classical communication cannot increase the quantum capacity of a pure-loss bosonic attenuation channel beyond the rate achievable by direct transmission. The proof introduces a notion of fractional extendibility for Gaussian states, establishes some of its properties, and uses them to bound the effective channel produced by any such repeater chain.

Significance. If the central claim holds, the result is significant because it resolves an open question on the utility of Gaussian repeaters for lossy optical channels and supplies a new analytic tool (fractional extendibility) tailored to Gaussian networks. The theorem is scoped precisely to the stated class of operations, and the introduction of the new framework is a clear strength that may enable further analyses of restricted repeater protocols.

minor comments (2)
  1. [Abstract] Abstract: the statement that the proof 'establishes some of its useful properties' would be clearer if it briefly indicated which properties (e.g., monotonicity under Gaussian maps or a specific bound on the extendibility parameter) are actually invoked in the no-go argument.
  2. [Introduction] The modeling choice that repeater nodes are limited exactly to Gaussian operations and homodyne detection is load-bearing; a short dedicated paragraph early in the introduction confirming that this restriction is both necessary for the theorem and experimentally motivated would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments appear in the provided report, so there are no individual points requiring point-by-point rebuttal or revision.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper introduces fractional extendibility as a novel generalization of k-extendibility tailored to Gaussian states, then derives the no-go theorem by applying its properties to repeater chains restricted to Gaussian operations and homodyne detection. This is a self-contained mathematical argument with no reduction of the central claim to fitted parameters, self-citation chains, or equations true by construction. The modeling restriction to Gaussian elements is explicitly scoped and load-bearing but does not create definitional circularity. No load-bearing steps match the enumerated patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the newly introduced definition of fractional extendibility together with standard facts about Gaussian states and bosonic loss channels.

axioms (2)
  • standard math Standard properties of Gaussian states, homodyne measurements, and pure-loss bosonic channels from quantum optics.
    Invoked throughout the proof framework described in the abstract.
  • ad hoc to paper The stated properties of the newly defined fractional extendibility hold for the relevant Gaussian states.
    This is the core new tool introduced to establish the no-go result.
invented entities (1)
  • Fractional extendibility no independent evidence
    purpose: To provide bounds on the performance of Gaussian repeater chains.
    New mathematical notion defined in the paper for analyzing Gaussian quantum networks.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Energetics of non-Gaussianity in single mode cavities

    quant-ph 2026-06 unverdicted novelty 5.0

    An energetic decomposition defines a non-Gaussianity measure for pure single-mode states that connects to relative entropy and serves as a witness for mixed states.

Reference graph

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