A high-dimensional quantum frequency converter

Baosen Shi; Chen Yang; Guangcan Guo; Shikai Liu; Shilong Liu; Yan Li; Yinhai Li; Zhaohuai Xu; Zhiyuan Zhou

REVIEW 4 major objections 6 minor 58 references

A high-dimensional quantum frequency converter

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper claims that a flat-top pump beam makes sum-frequency conversion efficiency nearly independent of OAM topological charge, yielding a frequency converter that preserves OAM qudits in 2, 3, and 5 dimensions.

desk verdict The flat-top pump for OAM qudit frequency conversion is a genuinely new idea and the experiment is a credible proof of principle, but the analytic core is not checkable as printed and the mode-flatness claim needs stronger experimental support. read the letter →

arxiv 1908.10569 v2 pith:6L7NHSC6 submitted 2019-08-28 quant-ph physics.app-phphysics.optics

Shilong Liu , Chen yang , Zhaohuai Xu , Shikai Liu , Yan Li , Yinhai Li , Zhiyuan Zhou , Guangcan Guo

show 1 more author

Baosen Shi

This is my paper · ORCID

classification quant-phphysics.app-phphysics.optics

keywords quantumfrequencyconversionorbitalangularmomentumquditsum-frequencygenerationflat-topbeamstatetomographyhigh-dimensionalcommunication

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that a quantum frequency converter can be made to work for high-dimensional orbital-angular-momentum (OAM) states, not just for two-dimensional qubits, by replacing the usual Gaussian pump beam with a flat-top beam. In sum-frequency generation, conversion efficiency for an OAM mode of topological charge $L$ ordinarily falls steeply as $|L|$ grows; the paper derives an analytic expression showing that a flat-top pump makes the normalized efficiency nearly independent of $L$ over a five-dimensional subspace. It backs this with a proof-of-principle experiment converting heralded single-photon OAM qudits from 1550 nm to 525 nm, reporting state fidelities of 98.29%, 97.42%, and 86.75% for dimensions 2, 3, and 5 without dark-count subtraction. The point of the claim is that such a converter could serve as an interface between OAM qudit sources and networks operating at different wavelengths, a step toward high-capacity quantum communication.

What carries the argument

The key machinery is the flat-top pump beam: a beam with uniform intensity over a disk of radius $w_{\rm FTB}$ and zero intensity outside, used as the classical pump in sum-frequency generation. The paper shows that with this pump the normalized conversion efficiency for an OAM eigenstate of charge $L$ is governed by an integral $h(L,\gamma)$ that depends on the beam-waist ratio $\gamma=w_p/w_i$, and that for $\gamma$ large enough the efficiency becomes almost $L$-independent. A $\pi$-shaper and Fourier lens generate the flat-top profile from a Gaussian beam, and a 10-mm PPKTP crystal performs the up-conversion. The argument treats the process as a spatial beam splitter in frequency: each OAM mode is up-converted with probability $\sin^2(\xi_L\tau)$, and equal $\xi_L$ across modes is what preserves the qudit.

What would settle it

Measure the per-mode conversion efficiency for OAM eigenstates $L=-2,\ldots,2$ as a function of pump propagation inside a longer crystal: if the flat-top profile diffracts appreciably within the crystal, the per-mode efficiencies will begin to separate, directly contradicting the claimed mode-independence. Equivalently, a Rayleigh-Sommerfeld propagation calculation of the shaped flat-top beam over the full crystal length that yields $L$-dependent efficiencies differing by more than the experimental error bars would settle the claim against the paper.

Watch

Extended reading notes

Core claim

The central discovery is that the normalized conversion efficiency of sum-frequency generation for an OAM eigenstate $|L\rangle$ becomes essentially flat in $L$ when a flat-top beam is used as the pump. For a Gaussian pump the efficiency is proportional to an integral $h(L,\xi)$ that shrinks rapidly with topological charge; for a flat-top pump the paper derives an analytic expression whose $L$-dependence is governed by the beam-waist ratio $\gamma=w_p/w_i$, and shows numerically and experimentally that over the subspace $L=-2,\ldots,2$ the per-watt conversion efficiency stays at about 0.33--0.42%/W. Treating the nonlinear crystal as a spatial beam splitter for OAM modes in the frequency domain, the mode-independence means each OAM component of a qudit is up-converted with nearly the same amplitude, preserving the encoded state. The authors demonstrate this by preparing infrared OAM qudits of dimension 2, 3, and 5, converting them to visible, and reconstructing the output density matrices by qudit quantum state tomography.

Load-bearing premise

The load-bearing premise is that the flat-top pump beam keeps its flat intensity profile over the full 10-mm length of the nonlinear crystal, so the mode-independent conversion-efficiency formula remains valid throughout the conversion.

Editorial extensions

If this is right

A single QFC can interface OAM qudits at different wavelengths without distorting the encoded state, so atomic-memory wavelengths and telecom fiber wavelengths can be linked in high-dimensional quantum networks.
Because the per-mode normalized efficiency is comparable to earlier Gaussian-pump QFCs, the approach does not sacrifice overall conversion efficiency in exchange for mode-independence.
The same flat-top-pump scheme should extend to higher-dimensional OAM subspaces, since the mode-independence removes the main obstacle that previously forced converters to stay two-dimensional.
The converter can operate in a low-power single-pass configuration, and the total efficiency can be raised by stronger pumps or cavity enhancement without changing the mode-independence.
The demonstrated qudit tomography in mutually unbiased bases provides a ready-made characterization tool for OAM qudit interfaces at other wavelengths.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same flat-top-pump principle likely applies to other nonlinear frequency-conversion processes that conserve OAM, such as difference-frequency generation or spontaneous parametric down-conversion, where Gaussian pumps also introduce OAM-dependent efficiencies.
If the flat-top assumption is the load-bearing part, any pump with a broad flat spatial profile, such as a top-hat or Bessel-like beam, should show a similar flattening in conversion efficiency, giving a testable family of pump shapes.
The fidelity drop from 98% to 86% between $d=2$ and $d=5$ is attributed in the paper mainly to collection efficiency and dark counts; with better mode sorting or lower-noise detectors, dimensions well beyond 5 should become accessible.
Because the input and output beam profiles look similar in the paper, the converter may also serve as an OAM-preserving image frequency converter, a new capability for nonlinear imaging.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this paper has a real new idea—use a flat-top pump to make the sum-frequency conversion efficiency nearly independent of OAM charge—and the experiment goes beyond prior work by handling d=3 and d=5 qudits, not just two-dimensional superpositions. The authors also report fidelities with and without dark counts, show interference visibilities, and include beam profiles. That transparency earns credit.

The soft spots are real but not fatal. The biggest one is Eq. (A6), the h(L,γ) integral that underpins the theoretical mode-independence claim. As printed, the L-dependent factor (L! − Γ(1+L,bγ²)) is independent of x and y, so it just multiplies a symmetric double integral; no radial overlap integral is left. This looks like a transcription error or a missing step, and it makes the central analytic prediction uncheckable. A referee should ask for the derivation or a corrected formula.

Second, the experimental n-CE values—0.37, 0.42, and 0.33 %/W for L=0,1,2—have no error bars. The peak-to-peak spread is about 25%, which is larger than the word “nearly equal” suggests. I would like to see uncertainties and a direct statement of the beam waist ratio γ used in the experiment.

Third, the flat-top beam is asserted to stay flat over the 10 mm crystal, but only the center profile is characterized. The authors concede the flat-top is not a paraxial-Helmholtz solution and will diffract; they say a simulation shows it remains flat, but that simulation is not shown in enough detail to check. This is a moderate concern because the theoretical model and simulated fidelities depend on that spatial invariance.

The d=5 fidelity of 86.75% without dark counts and 67.04% with them is modest, as the authors admit. Their explanation—mode-dependent collection efficiency in projection measurements—is plausible and they give the relevant numbers. I do not consider this a flaw so much as an honest limitation of a proof-of-principle demonstration.

On balance, the central claim is likely right: the flat-top pump does flatten the conversion efficiency across low OAM modes, and the paper is an honest step toward high-dimensional frequency interfaces. The citation pattern looks fine; the self-citations are to their own prior QFC work, which is appropriate.

Who is this for? Anyone working on OAM-based quantum networks or quantum frequency conversion. It deserves a serious referee, not a desk reject. My recommendation: send it to peer review, and require the authors to fix or derive Eq. (A6), add error bars to the n-CE measurements, and give a clearer account of the flat-top beam profile inside the crystal. With those changes, I would be happy to cite it.

Referee Report

4 major / 6 minor

Summary. The manuscript reports the first demonstration of a high-dimensional quantum frequency converter for orbital angular momentum (OAM) qudits, using sum-frequency generation pumped by a flat-top beam in a 10 mm PPKTP crystal. The authors derive an analytic expression for the normalized conversion efficiency (n-CE) for a flat-top pump, claim that the efficiency is nearly independent of the OAM topological charge L, and support this with measurements of n-CE for L=0,1,2 and with quantum state tomography of converted qudits in dimensions 2, 3, and 5, reporting fidelities of 98.29%, 97.42%, and 86.75% (without dark counts).

Significance. If the central claim holds, this is a meaningful advance: it would provide a frequency interface for high-dimensional OAM states, an important missing component for high-capacity quantum networks connecting atomic memories and fiber channels. Strengths of the paper include the parameter-free theoretical model based on coupled-wave equations, the explicit reporting of experimental parameters (wavelengths, crystal length, beam waists), the direct measurement of conversion efficiencies for different OAM modes, and the transparent presentation of fidelities both with and without dark-count subtraction. The experimental demonstration of mode-flat conversion efficiency for low-order OAM modes is valuable regardless of the analytic formula. However, the analytic mode-flatness claim is currently not fully checkable because of the incomplete expression for h(L,γ) and the unverified assumption of flat-top propagation over the crystal length.

major comments (4)

[Appendix A, Eq. (A6)] The expression for h(L,γ) in Eq. (A6) is not derived, and as printed it cannot yield the claimed L-dependent mode-flatness. The factor (L! − Γ(1+L,bγ²)) is independent of x and y, so it factors out of the double integral; the remaining integrand (1+ix/ZI + 1−iy/ZI) integrates to a constant plus an odd term that vanishes over symmetric limits. The resulting h(L,γ) would be proportional to (L! − Γ(1+L,bγ²)) times a constant, which does not by itself reproduce a flat response. Please provide the complete derivation, including the radial integration over the flat-top profile and the definition of the parameter b, or else the theoretical basis for Eq. (5) and Fig. 1 is uncheckable.
[Section II and Appendix A] The assertion that the flat-top beam 'still keeps a flat profile within 10 mm' is not demonstrated. The manuscript acknowledges that the flat-top beam is not a paraxial-Helmholtz solution and will diffract, but it does not provide simulated intensity profiles along the propagation direction or a quantitative estimate of the resulting change in the mode-dependence of the conversion efficiency. Because Eq. (5) and the simulated fidelities in Fig. 4 assume a spatially invariant flat-top profile, this assumption is load-bearing and needs support, e.g., by numerical propagation using the Rayleigh-Sommerfeld integral already cited.
[Section III.B] The n-CE values reported for L=0,1,2 (0.37, 0.42, and 0.33 %/W) are presented without error bars or a statistical analysis. The observed peak-to-peak spread is about 25% of the mean, which is not obviously consistent with the claim that the n-CE is 'nearly equal' for these modes. Please provide uncertainties (e.g., from Poisson statistics of the measured counts and power calibration) and, if possible, a test of whether the differences are significant.
[Section III.C] The d=5 fidelity without dark counts is 86.75%, but drops to 67.04% when dark counts are included. Since the high-dimensional claim rests on the five-dimensional quantum state tomography, the manuscript should discuss explicitly whether the raw (with-dark-count) fidelity meets the standard of a 'high-quality' QFC, and justify the accidental-count subtraction beyond the statement that it is 'reasonable'.

minor comments (6)

[Section II, Eq. (1)] The sum in Eq. (1) is over ℜ but ξ_L is subscripted with L; please use consistent notation.
[Section III.B] The phrase 'the input being a week coherent laser' should read 'weak coherent laser'.
[Fig. 4 table] The row labels 'Gaussian-beam-T', 'Flattop-beam-T', and 'Flattop-beam-E' are not defined; please spell out 'T' and 'E' (presumably theory and experiment) and align the entries with the columns.
[Appendix B, Eq. (B3)] The symbol ω_d is not defined; please define ω_d = exp(2πi/d).
[Appendix A] The word 'topologic' appears in several places; it should be 'topological'.
[Fig. 1 caption] The term 'c-CEs' in the Fig. 1 caption is not defined; it presumably should be 'n-CEs'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the flat-top-pump mode-independence claim follows from coupled-wave equations with stated experimental parameters and is checked against independently measured conversion efficiencies and tomographic fidelities.

full rationale

The paper's central derivation chain is self-contained. The flat-top pump is defined independently as a uniform-intensity beam in Eq. (4), and the flat-top n-CE in Eq. (5)/Appendix A is obtained from the standard nonlinear coupled-wave equations (A1) with the stated experimental parameters (wavelengths, crystal length, beam waist). The predicted mode-insensitivity is then compared with measured n-CEs in Sec. III.B (0.37, 0.42, 0.33 %/W for L=0,1,2) and with quantum-state-tomography fidelities in Sec. III.C. No parameter is fitted to the reported fidelities and then renamed as a prediction; the theoretical fidelities in Fig. 4 are simulations from the same physical model, while the experimental fidelities are reconstructed from independent coincidence measurements. The self-citations to the authors' earlier work (Refs. [2,4,23,39,41]) supply Gaussian-pump baselines and OAM state-preparation methods, but the flat-top result does not reduce to those citations by construction. The main caveats are correctness risks rather than circularity: the printed form of h(L,γ) in Eq. (A6) appears to have a transcription issue because the L-dependent prefactor is independent of x,y and the remaining linear terms integrate to constants, making the analytic expression difficult to check; the assumption that the π-shaper flat-top profile 'still keeps a flat profile within 10 mm' is asserted in Sec. II and Appendix A rather than measured inside the crystal; and the experimental n-CEs in Table 1 are given without error bars. These affect confidence in the derivation and quantitative claims, but they do not make the prediction equivalent to its inputs.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central derivation introduces no fitted constants. The key supporting assumptions are experimental geometry (flat-top beam shape preservation) and an azimuthal symmetry assumption for negative OAM modes. The remaining parameters are standard wavelengths, crystal length, and nonlinear coefficients taken from the prior literature.

free parameters (1)

Flat-top beam waist ratio gamma = w_p / w_i
The flatness of the conversion efficiency with OAM order is controlled by this ratio (Fig. 1c and Fig. 1d). The experimental value is not stated explicitly, so the demonstrated mode-flatness is conditional on an unreported beam geometry.

assumptions (4)

standard math The coupled-wave equations (A1) describe the sum-frequency generation process with the stated phase-matching condition.
Standard nonlinear optics model used to compute the normalized conversion efficiency.
domain assumption The flat-top beam profile of Eq. (4) is preserved over the crystal length.
Asserted in Section II as 'still keeps a flat profile within 10 mm'; required for Eq. (5) to apply.
domain assumption Negative OAM modes have the same conversion efficiency as positive OAM modes.
Appendix A states that the n-CE for a negative OAM state is calculated from the corresponding positive OAM state, assuming azimuthal symmetry of the setup; this is not separately measured.
standard math The mutually unbiased bases generated by Eq. (B3) form a complete tomography basis for prime dimensions.
Standard construction used for quantum state tomography of the converted qudit.

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Cite this review

Pith. "Pith review of A high-dimensional quantum frequency converter." pith.science (2026). https://pith.science/paper/6L7NHSC6

@misc{pith2026190810569,
  author       = {Pith},
  title        = {Pith review of: A high-dimensional quantum frequency converter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6L7NHSC6}},
  note         = {Machine review of arXiv:1908.10569}
}

read the original abstract

In high dimensional quantum communication networks, quantum frequency convertor (QFC) is indispensable as an interface in the frequency domain. For example, many QFCs have been built to link atomic memories and fiber channels. However, almost all of QFCs work in a two-dimensional space. It is still a pivotal challenge to construct a high-quality QFC for some complex quantum states, e.g., a high dimensional single-photon state that refers to a qudit. Here, we firstly propose a high-dimensional QFC for an orbital angular momentum qudit via sum frequency conversion with a flat top beam pump. As a proof-of-principle demonstration, we realize quantum frequency conversions for a qudit from infrared to visible range. Based on the qudit quantum state tomography, the fidelities of converted state are 98.29(95.02)\%, 97.42(91.74)\%, and 86.75(67.04)\% for a qudit without (with) dark counts in 2,3, and 5 dimensions, respectively. The demonstration is very promising for constructing a high capacity quantum communication network.

Figures

Figures reproduced from arXiv: 1908.10569 by the authors.

**Figure 2.** FIG. 2. Schematics of a HD-QFC. a: Generation of an infrared heralding single-photon state. b: the HD-QFC for a qudit [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** FIG. 4. The reconstructed density matrix and the fi [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (1 more)

**Figure 5.** Figure 5: FIG. 5. The conversion efficiency and beam profiles for a high-dimensional frequency converter (HD-FC). (a)-(b): Conversion [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Continue with ORCID to comment.

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e, f: are the situations of a qudit |ϕ⟩ℜ=5= (|−2⟩ +|−1⟩ +|0⟩ +|1⟩ +|2⟩)/ √ 5 in ﬁve- dimensional subspace

c, d: The real and imaginary part of the density matrix for a three-dimensional state |ϕ⟩ℜ=3 (|−1⟩ +|0⟩ +|1⟩)/ √ 3 . e, f: are the situations of a qudit |ϕ⟩ℜ=5= (|−2⟩ +|−1⟩ +|0⟩ +|1⟩ +|2⟩)/ √ 5 in ﬁve- dimensional subspace. Each coincidence data for three qudits are recorded at 100s, 300s, and 300s, respectively. The cor- responding dark counts are 16, 20...

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A high-dimensional quantum frequency converter

The main diﬃculty is that the con- version eﬃciency (CE) of FC usually strongly depends on the topological charge|L| (decreasing exponentially with |L| [2–4, 23–25]). This drawback prevents one from build- ing up a high ﬁdelity interface between photonic qudit in the diﬀerent frequency domains. For example, in quan- tum networks with both quantum memories...

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