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arxiv: 2604.20103 · v1 · submitted 2026-04-22 · 🪐 quant-ph

Universality cost of non-Gaussian enhancement in continuous-variable quantum teleportation: A fidelity--deviation trade-off

Kyoungho Cho , Bongjune Kim , Jeongho Bang This is my paper

Pith reviewed 2026-05-10 01:14 UTC · model grok-4.3

classification 🪐 quant-ph
keywords continuous-variable quantum teleportationfidelity deviationdisplacement covariancenon-Gaussian resourcesnoiseless linear amplificationtrade-offheralded protocols
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The pith

Any deterministic unity-gain displacement-covariant teleportation channel has vanishing fidelity deviation for coherent-state benchmarking, whether its entangled resource is Gaussian or non-Gaussian.

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

The paper proves that deterministic unity-gain teleportation channels obeying displacement covariance deliver identical fidelity for every coherent-state input, so the deviation across inputs is exactly zero. This zero-deviation property survives even when the shared entanglement is non-Gaussian. Nonzero deviation therefore flags a loss of covariance rather than the use of non-Gaussian resources. When average fidelity is raised by input-selective post-selection, such as measurement-based noiseless linear amplification, the deviation rises in step with the fidelity gain and the success probability falls.

Core claim

Any deterministic unity-gain teleportation channel that is displacement covariant has vanishing fidelity deviation for coherent-state benchmarking, irrespective of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation therefore diagnoses covariance breaking rather than non-Gaussianity. When a protocol raises the average fidelity through input-selective conditioning, the deviation generically increases in tandem, giving a quantitative universality cost, as illustrated by teleportation enhanced by measurement-based noiseless linear amplification where stronger filtering concentrates successful events and suppresses the heralding rate.

What carries the argument

The fidelity deviation, which quantifies input dependence of single-shot teleportation fidelity, together with the displacement covariance condition on the channel that forces the deviation to zero for coherent states.

If this is right

  • Nonzero fidelity deviation in these channels indicates broken displacement covariance rather than non-Gaussian resources.
  • Raising average fidelity by input-selective conditioning necessarily increases fidelity deviation.
  • The trade-off links higher conditional fidelity to lower success probability and reduced input uniformity.
  • Stronger heralded filters improve fidelity only by concentrating successful events in favored phase-space regions.

Where Pith is reading between the lines

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

  • Protocols that claim non-Gaussian improvement must separately verify that covariance is preserved if uniformity is required.
  • In optical networks or measurement-based architectures, low deviation ensures consistent performance across all inputs.
  • The framework can be used to test whether observed fidelity gains are genuine channel improvements or selectivity artifacts.

Load-bearing premise

The teleportation channel must be deterministic and unity-gain, displacement covariant, and benchmarked on coherent states.

What would settle it

A direct measurement of input-dependent fidelity variation in any deterministic unity-gain displacement-covariant teleportation protocol using coherent states would falsify the vanishing-deviation result.

Figures

Figures reproduced from arXiv: 2604.20103 by Bongjune Kim, Jeongho Bang, Kyoungho Cho.

Figure 1
Figure 1. Figure 1: FIG. 1. Single-shot conditional fidelity profile [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Trade-off curves in the [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
read the original abstract

Continuous-variable (CV) quantum teleportation is usually benchmarked by average fidelity, but when the teleportation is repeatedly used within optical networks or measurement-based architectures, uniformity across the input ensemble becomes equally important. We analyze this issue using two complementary figures of merit: the average fidelity and the fidelity deviation, which quantifies the input dependence of the single-shot teleportation fidelity. We prove that any deterministic unity-gain teleportation channel that is displacement covariant has vanishing fidelity deviation for coherent-state benchmarking, irrespective of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation therefore diagnoses covariance breaking rather than non-Gaussianity. We then show that when a protocol raises the average fidelity through input-selective conditioning, the deviation generically increases in tandem, giving a quantitative universality cost. As a concrete example, we study teleportation enhanced by the so-called measurement-based noiseless linear amplification, where a heralded filter acts on the Bell-measurement record. The resulting trade-off among average fidelity, fidelity deviation, and success probability shows that stronger filtering can improve the conditional fidelity only by concentrating the successful events in favored regions of phase space, thereby suppressing the success probability and reducing input uniformity. Our results provide an operational framework for distinguishing genuine channel improvement from selectivity-driven post-selected advantage and suggest that the probabilistic CV teleportation should be assessed with average quality, universality, and heralding rate treated on an equal footing.

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 paper introduces fidelity deviation as a complementary figure of merit to average fidelity for assessing continuous-variable teleportation. It proves that any deterministic unity-gain displacement-covariant teleportation channel yields identically zero fidelity deviation when benchmarked on coherent states, independent of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation is therefore a signature of covariance breaking. The work then derives a quantitative trade-off showing that input-selective conditioning to raise conditional average fidelity generically increases deviation, and illustrates this with a heralded measurement-based noiseless linear amplification protocol, where stronger filtering improves conditional fidelity only at the expense of reduced success probability and input uniformity.

Significance. If the covariance-based proof and the subsequent trade-off analysis hold, the manuscript supplies a useful operational framework for distinguishing genuine channel improvements from selectivity-driven advantages in probabilistic CV protocols. This is relevant for network applications and measurement-based architectures where uniformity across inputs matters. The explicit example with noiseless linear amplification makes the trade-off concrete and suggests that average fidelity, deviation, and heralding rate should be treated on equal footing.

minor comments (2)
  1. §3, around the statement of the main theorem: the proof that covariance implies α-independent fidelity is direct from the displacement conjugation argument, but the manuscript should add one sentence clarifying that the argument assumes the channel is trace-preserving (which is already implicit in the deterministic unity-gain condition).
  2. Figure 3 caption and surrounding text: the plotted trade-off curves for different filter strengths would benefit from an explicit statement of the numerical integration method used to obtain the conditional fidelity and deviation values.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation for minor revision. The referee's summary accurately captures the central results on fidelity deviation and the trade-off in conditional CV teleportation protocols.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The manuscript's core claim is a direct mathematical consequence of the definitions of displacement covariance, deterministic unity-gain channels, and single-shot fidelity on coherent states: conjugating the channel by displacement operators maps any coherent input to the vacuum case while preserving overlap, forcing the fidelity to be input-independent and thus the deviation to vanish. This holds for arbitrary resources (Gaussian or non-Gaussian) and does not invoke fitted parameters, self-referential equations, or load-bearing self-citations that reduce the result to its own inputs. The subsequent trade-off for conditional protocols follows from the same covariance framework applied to heralded filtering, with all assumptions (determinism, unity gain, coherent-state benchmarking) stated explicitly and the result falsifiable by counter-example channels that break covariance. No step reduces by construction to a prior fit or self-citation chain; the derivation is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract alone, the claims rest on standard definitions of fidelity, covariance, and coherent-state benchmarking with no additional free parameters, ad-hoc axioms, or invented entities introduced.

pith-pipeline@v0.9.0 · 5563 in / 1114 out tokens · 31944 ms · 2026-05-10T01:14:32.401640+00:00 · methodology

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Reference graph

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