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arxiv: 2404.06438 · v6 · pith:7ZM3WWHJnew · submitted 2024-04-09 · 🪐 quant-ph

Non-Gaussian state teleportation with a nonlinear feedforward

Vojt\v{e}ch Kala , Mattia Walschaers , Radim Filip , Petr Marek This is my paper

Pith reviewed 2026-05-24 01:56 UTC · model grok-4.3

classification 🪐 quant-ph
keywords non-Gaussian statesnonlinear feedforwardcluster statesquantum teleportationcontinuous-variable systemsnonlinear squeezingmeasurement-based quantum computation
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The pith

Nonlinear feedforward reduces added noise when teleporting non-Gaussian states through cluster states.

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

The paper analyzes how a quantum non-Gaussian state carrying nonlinear squeezing propagates through a small continuous-variable cluster state during measurement-induced quantum computation. It shows that a nonlinear feedforward control in the deterministic teleportation protocol cuts the noise added by imperfect entanglement and preserves more of the nonlinear squeezing. The same improvement appears in a probabilistic version of the protocol. This enhancement can be realized with present-day experimental resources in the probabilistic case. Better non-Gaussian state processing supports the required combination of cluster states and non-Gaussianity for quantum computation.

Core claim

A nonlinear feedforward in the deterministic teleportation protocol reduces the added noise and improves the nonlinear squeezing transferred through a small cluster state. In a probabilistic regime, the improvement can be manifested even with current experimental resources.

What carries the argument

The nonlinear feedforward operation, which applies a nonlinear correction to the measurement outcomes to counteract noise during teleportation of the state through the cluster.

If this is right

  • Reduced added noise in deterministic teleportation of non-Gaussian states.
  • Improved transfer of nonlinear squeezing through the cluster state.
  • The improvement appears in a probabilistic regime using current experimental resources.
  • Better processing of non-Gaussian states advances the interplay with cluster states needed for quantum computation.

Where Pith is reading between the lines

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

  • The technique could scale to larger cluster states to support more complex non-Gaussian operations in measurement-based computation.
  • Probabilistic demonstrations may provide near-term tests of the noise reduction.
  • Nonlinear feedforward might apply to noise mitigation in other continuous-variable protocols.

Load-bearing premise

The model of noise propagation through the small cluster state and the nonlinear feedforward accurately represents the dominant imperfections without extra noise from the correction itself.

What would settle it

An experiment implementing teleportation of a non-Gaussian state both with and without the nonlinear feedforward that measures no reduction in added noise or no gain in transferred nonlinear squeezing would falsify the central claim.

Figures

Figures reproduced from arXiv: 2404.06438 by Mattia Walschaers, Petr Marek, Radim Filip, Vojt\v{e}ch Kala.

Figure 1
Figure 1. Figure 1: a) Optical scheme illustrating the considered cluster state generation. b) Optical scheme showing the nonlinear cubic phase measurement applied to one part of the cluster state to project it onto the cubic state. The measurement is decomposed into an ideal cubic nonlinearity followed by homodyne measurement. The measurement result is used in a feedforwarded displacement on the second mode. c) Regular telep… view at source ↗
Figure 2
Figure 2. Figure 2: a) Nonlinear squeezing at the output mode, expressed in dB (3). The Gaussian squeezing, available for the preparation of the cluster state and the state (6), is limited to a certain value [dB] during optimization. The limit is shown on the horizontal axis. The two-mode cluster state is pure and optimized for each scheme. Output nonlinear squeezing is shown for deterministic regular and nonlinear teleportat… view at source ↗
Figure 3
Figure 3. Figure 3: a) Nonlinear squeezing at the output mode, expressed in dB (3). The Gaussian squeezing, available for the preparation of the cluster state and the state (6), is limited to a certain value [dB] during optimization. The limit is shown on the horizontal axis. The two-mode cluster state carries n = 0.1 additional thermal noise. To better see the comparison with the case of a pure cluster state (Fig. 2a), the l… view at source ↗
Figure 4
Figure 4. Figure 4: Nonlinear squeezing teleported by linear (dotted line) and nonlinear (solid line) teleportation. The input state and parameters of the optical scheme are optimized for the deterministic scenario. Quantum states depending on the measurement results with best nonlinear squeezing are aggregated up to a given probability [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Scheme for conditioned regular/nonlinear teleportation [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Nonlinear squeezing (23) produced by unity gain regular/nonlinear teleportation of an eigen￾state of the operator in Eq. O (1) conditioned on measurement results of the homodyne measurement with best results aggregated up to some probability and evaluated at native cubicity of the state before teleportation. The nonlinear teleportation and regular teleportation were simulated with two mode squeezed vacuum … view at source ↗
read the original abstract

Measurement-induced quantum computation with continuous-variable cluster states utilizes teleportation to transmit and alter quantum states via measurement-and-feedforward control. One of the key challenges of this approach is the deterioration of quantum states caused by the noise added due to imperfect entanglement of the cluster. We analyze the propagation of a quantum non-Gaussian state with nonlinear squeezing through a small cluster state. We show that a nonlinear feedforward in the deterministic teleportation protocol reduces the added noise and improves the nonlinear squeezing transferred. In a probabilistic regime, the improvement can be manifested even with current experimental resources. Better processing of non-Gaussian states can bring us closer to the necessary interplay between cluster states and non-Gaussianity required by quantum computing.

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

1 major / 1 minor

Summary. The manuscript analyzes propagation of a non-Gaussian state possessing nonlinear squeezing through a small continuous-variable cluster state in a measurement-induced quantum computation protocol. It claims that replacing linear feedforward with a nonlinear feedforward operation in the deterministic teleportation step reduces the net added noise and thereby improves the transferred nonlinear squeezing; a probabilistic variant is asserted to yield visible improvement with present-day experimental resources.

Significance. If the idealized nonlinear feedforward model is shown to capture the dominant experimental imperfections without introducing additional unmodeled noise, the result would constitute a concrete, implementable improvement in the handling of non-Gaussian resources within cluster-state architectures, directly addressing one of the central obstacles to scalable continuous-variable quantum computation.

major comments (1)
  1. [Noise propagation model and nonlinear feedforward definition] The central claim that nonlinear feedforward reduces added noise relative to linear feedforward (and thereby improves transferred nonlinear squeezing) rests on the assumption that the chosen functional form introduces no dominant extra quadrature noise, higher-order distortions, or resource overhead beyond the modeled cluster-state imperfections. This modeling choice is load-bearing for both the deterministic and probabilistic analyses and requires explicit validation or sensitivity analysis.
minor comments (1)
  1. [Abstract] The abstract would benefit from a single quantitative statement of the improvement (e.g., the factor by which nonlinear squeezing is enhanced or the reduction in added noise variance) to allow readers to gauge the practical scale of the effect.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our analysis of nonlinear feedforward in continuous-variable cluster-state teleportation. We address the single major comment below.

read point-by-point responses

  1. Referee: [Noise propagation model and nonlinear feedforward definition] The central claim that nonlinear feedforward reduces added noise relative to linear feedforward (and thereby improves transferred nonlinear squeezing) rests on the assumption that the chosen functional form introduces no dominant extra quadrature noise, higher-order distortions, or resource overhead beyond the modeled cluster-state imperfections. This modeling choice is load-bearing for both the deterministic and probabilistic analyses and requires explicit validation or sensitivity analysis.

    Authors: We agree that the idealized nonlinear feedforward constitutes a modeling assumption whose validity must be examined. In the manuscript the nonlinear feedforward is defined to apply the exact inverse of the nonlinear squeezing operation, thereby canceling the leading-order effect of the cluster-state noise on the non-Gaussian resource without introducing additional quadrature noise within the model. This choice isolates the benefit relative to linear feedforward. Nevertheless, the referee correctly notes that real implementations could add higher-order distortions or overhead. In the revised manuscript we will add an explicit sensitivity analysis that perturbs the nonlinear feedforward function with small quadrature noise, cubic and quartic distortions, and finite squeezing overhead, quantifying the resulting degradation of transferred nonlinear squeezing for both the deterministic and probabilistic protocols. This addition will make the load-bearing assumption transparent and will delineate the regime in which the reported improvement remains observable with present-day resources. revision: yes

Circularity Check

0 steps flagged

No circularity: modeling outcome independent of inputs

full rationale

The paper models noise propagation through a small cluster state under linear versus nonlinear feedforward for non-Gaussian teleportation. The reported reduction in added noise and improvement in transferred nonlinear squeezing follow from explicit propagation equations and protocol definitions rather than any self-definitional equivalence, fitted parameter re-labeled as prediction, or load-bearing self-citation chain. No quoted step reduces the central claim to its own inputs by construction; the analysis remains self-contained against external benchmarks of cluster noise and feedforward operations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The abstract relies on standard continuous-variable quantum optics models for cluster states and teleportation; no new free parameters, axioms, or invented entities are introduced at the level of the abstract.

axioms (1)
  • standard math Standard quantum mechanics and continuous-variable formalism for Gaussian and non-Gaussian states
    Used to model cluster-state entanglement and measurement-induced teleportation.

pith-pipeline@v0.9.0 · 5652 in / 1182 out tokens · 20073 ms · 2026-05-24T01:56:28.168792+00:00 · methodology

discussion (0)

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