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arxiv: 2607.02427 · v1 · pith:7UF47YW6new · submitted 2026-07-02 · 🪐 quant-ph

Optimal stellar rank approximation of squeezed cat states with photon catalysis

Julian K. Nauth , Nathan Walk , Ananga M. Datta , Kurt Busch , Jens Eisert , Oliver Benson , Roger A. K\"ogler This is my paper

Pith reviewed 2026-07-03 11:33 UTC · model grok-4.3

classification 🪐 quant-ph
keywords photon catalysissqueezed cat statesstellar ranknon-Gaussian quantum statesbosonic quantum resourcesfidelity optimizationquantum error correctionoptical losses
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The pith

Photon catalysis between Fock states and squeezed states achieves provably optimal fidelity to squeezed cat states in identified regimes.

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

The paper examines photon catalysis protocols that combine low-number Fock states with squeezed states to produce squeezed cat states. It applies the stellar rank formalism to quantify the non-Gaussian complexity of the inputs and outputs, then compares the fidelity of the generated states against the highest fidelity any protocol could reach with the same resources. This comparison reveals cases where the catalysis steps are optimal and locates parameter regimes that deliver high-fidelity approximations while keeping resource costs low. The work also contrasts these protocols with Gaussian boson sampling-inspired methods, notes advantages from deterministic Fock sources, and models the effect of optical losses on the output quality.

Core claim

The catalysis protocols considered here are provably optimal in identified instances because their output fidelity matches the maximum attainable by any protocol that consumes inputs of identical stellar rank. Parameter regimes exist in which high-fidelity approximations of the target squeezed cat states are obtained with minimal non-Gaussian resources. The same framework extends to related states such as squeezed Fock states, and loss effects are quantified through Hilbert-space truncation.

What carries the argument

Stellar rank, a numerical measure of non-Gaussian complexity for states and measurements that enables direct comparison of achieved fidelity to the theoretical maximum possible with given input resources.

If this is right

  • Certain catalysis protocols reach the highest fidelity allowed by their input stellar ranks.
  • High-fidelity squeezed cat states become accessible with low non-Gaussian resource overhead in specific parameter windows.
  • Photon catalysis using deterministic Fock sources shows higher success probability and state quality than selected Gaussian boson sampling-inspired alternatives.
  • Modeled optical losses reduce fidelity in a quantifiable way that still leaves usable states in the identified regimes.
  • The same stellar-rank comparison applies to the generation of squeezed Fock states needed for quantum error correction.

Where Pith is reading between the lines

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

  • Stellar rank offers a practical benchmark that future non-Gaussian generation schemes in optics could adopt for optimality checks.
  • The loss-robustness results indicate concrete fidelity thresholds experimenters can target when designing heralded sources.
  • Extending the same resource-counting method to other heralded operations could clarify trade-offs across a wider set of bosonic protocols.

Load-bearing premise

The stellar rank formalism provides a complete and faithful characterization of non-Gaussian complexity that permits direct comparison of achieved fidelity to the maximum fidelity attainable by any protocol using the same input resources.

What would settle it

An alternative protocol that produces higher fidelity to the same target squeezed cat state while consuming inputs of equal or lower stellar rank would falsify the optimality claims.

Figures

Figures reproduced from arXiv: 2607.02427 by Ananga M. Datta, Jens Eisert, Julian K. Nauth, Kurt Busch, Nathan Walk, Oliver Benson, Roger A. K\"ogler.

Figure 1
Figure 1. Figure 1: FIG. 1. Photon catalysis comprising the interference of a squeezed [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Top: Wigner representation of the target state indicated by [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Optimum approximation between the catalysis output state [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Representations of Wigner functions of even cat states [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dependence of the stellar fidelity [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Dependence of the cat amplitude [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Dependence of the success probabilities [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Dependence of the success probability [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Loss modeling in photon catalysis for an input squeezed [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Effect of single channel losses to the output state [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Multi channel loss analysis. Each point represents a combination of loss budgets [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Numerical influence of different output state data sets to [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Comparison between the fidelity maximization of the output [PITH_FULL_IMAGE:figures/full_fig_p022_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Fidelity maximization of the output state to an arbitrary cat [PITH_FULL_IMAGE:figures/full_fig_p022_19.png] view at source ↗
read the original abstract

Non-Gaussian quantum states and operations constitute essential resources for achieving quantum computational advantage and enabling quantum error correction in bosonic platforms. However, their generation in optical settings remains a challenging experimental task, often relying on probabilistic heralded protocols. Here, we present an in-depth analysis of the suitability of photon catalysis between low number Fock states and squeezed states for the generation of squeezed coherent state superpositions. We employ the stellar rank formalism to characterize the non-Gaussian complexity of input resources (including both states and measurements) and the generated states. This enables a systematic comparison of the fidelity between the catalyzed output and the target states to the maximum fidelity achievable by any protocol with the same non-Gaussian input resources. In this sense, we identify instances where the catalysis protocols considered here are provably optimal. We identify parameter regimes in which high-fidelity approximations of the target states can be achieved with minimal resources. Furthermore, we benchmark the performance of photon catalysis against Gaussian boson sampling-inspired protocols in terms of success probability and state quality, highlighting the advantages of deterministic Fock state sources. We also investigate the generation of related non-Gaussian resources including squeezed Fock states relevant for quantum error correction. To account for experimental imperfections, we model losses across all optical modes using a Hilbert space truncation approach in the Fock basis and analyze the robustness of the generated states under realistic conditions. Our results quantify the trade-offs between non-Gaussian resource complexity, achievable fidelity, and losses in photon catalysis protocols, providing practical guidelines for near-term photonic implementations.

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 photon catalysis between low-number Fock states and squeezed states for generating squeezed cat states (squeezed coherent-state superpositions). It employs the stellar-rank formalism to quantify non-Gaussian complexity of inputs and outputs, enabling direct comparison of achieved fidelity against the maximum fidelity attainable by any protocol using identical stellar-rank resources. The work identifies parameter regimes of provable optimality, benchmarks catalysis against Gaussian-boson-sampling-inspired protocols, examines generation of squeezed Fock states, models uniform losses via Fock-basis truncation, and extracts practical guidelines for near-term photonic implementations.

Significance. If the optimality claims are rigorously established, the results supply concrete resource-fidelity-loss trade-offs and identify high-fidelity, low-resource regimes for non-Gaussian state preparation, directly relevant to bosonic quantum error correction and photonic advantage experiments. Explicit credit is due for the systematic stellar-rank comparison framework and the Hilbert-space truncation loss model, both of which strengthen the practical utility of the findings.

major comments (1)
  1. [Abstract] Abstract (and the corresponding results section on stellar-rank comparisons): the central claim that 'instances where the catalysis protocols considered here are provably optimal' are identified requires an explicit, general upper bound on fidelity that depends only on the stellar ranks of the input states and measurements (independent of squeezing parameter values). The manuscript must derive or cite such a bound; otherwise the optimality statements rest on numerical matching rather than a rank-based completeness argument.
minor comments (1)
  1. The loss-modeling section should report the specific truncation dimension N_trunc used in all fidelity calculations together with a convergence check (e.g., fidelity change when N_trunc is increased by 2).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and constructive feedback. Below we respond point-by-point to the major comment.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the corresponding results section on stellar-rank comparisons): the central claim that 'instances where the catalysis protocols considered here are provably optimal' are identified requires an explicit, general upper bound on fidelity that depends only on the stellar ranks of the input states and measurements (independent of squeezing parameter values). The manuscript must derive or cite such a bound; otherwise the optimality statements rest on numerical matching rather than a rank-based completeness argument.

    Authors: We agree that the presentation of optimality would benefit from greater clarity on how the upper bound is obtained. The stellar-rank measure is independent of Gaussian parameters, and for each fixed combination of input stellar ranks we compute the maximum fidelity to the target by numerically optimizing over all states and measurements possessing exactly those ranks (with arbitrary Gaussian operations permitted). When the catalysis protocol achieves this numerically determined maximum, the result is optimal with respect to the given non-Gaussian resources. This procedure constitutes a rank-based completeness argument for the low-rank cases examined, although the numerical value of the bound necessarily depends on the target squeezing. We will revise the abstract and the stellar-rank comparison section to (i) explicitly describe the optimization used to establish the rank-constrained fidelity upper bound and (ii) replace the phrase “provably optimal” with “optimal with respect to the numerically computed maximum fidelity attainable at the same stellar ranks.” No general closed-form analytical bound independent of all parameters appears to be available in the literature; the numerical approach is rigorous for the regimes considered. revision: yes

Circularity Check

0 steps flagged

No circularity: stellar-rank fidelity bound treated as external benchmark

full rationale

The paper's central claim rests on comparing catalyzed-state fidelity against a maximum fidelity attainable with identical stellar-rank resources. No quoted step reduces this maximum to a fitted parameter, self-defined quantity, or self-citation chain; the formalism is invoked to supply an independent upper bound rather than to rename or reconstruct the protocol output. Self-citations, if present, are not load-bearing for the optimality statements. The derivation therefore remains self-contained against the stated external benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; the central comparison rests on the domain assumption that stellar rank fully captures non-Gaussian complexity for optimality bounds. No free parameters or invented entities are mentioned.

axioms (1)
  • domain assumption Stellar rank formalism fully characterizes non-Gaussian complexity of states and measurements for fidelity comparisons
    Invoked to identify provably optimal instances and minimal-resource regimes.

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    Since PC and the GBS-like scheme both provide optimal stellar rank approximations, only the success probability re- mains for comparison. As suggested in Eq. (33), we investi- gate(m, n) =(1,1), (1,2), (2,1) and compare them to GBS- like scheme with the same stellar rank, i.e.,n= 2andn= 3, respectively. In particular, this covers examples for even and odd...

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