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Temporal modes of quantum states of light scattered by a two-level system

T0 review · 1 major / 0 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read Scattering single-mode two-photon light off a two-level system produces approximate two-mode NOON states.

desk verdict Analytic input-output map for temporal modes is the clear new piece; NOON approximation claim lacks any reported fidelity or error numbers. read the letter →

arxiv 2606.29974 v1 pith:VRKF6HY7 submitted 2026-06-29 quant-ph

Yann Bouchereau , Lucas Weitzel , Valerian Thiel , Valentina Parigi , Mattia Walschaers , Nicolas Treps This is my paper · ORCID
classification quant-ph
keywords quantumopticstwo-levelsystemtemporalmodesNOONstatesnon-GaussianscatteringWignernegativityentanglement
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

The paper derives an analytic description of the quantum state of light after scattering from a two-level system, expressed directly in terms of the input temporal modes. This description applies to multimode and multiphoton inputs. For the case of two photons entering in one temporal mode, numerical decomposition of the output into principal modes shows it approximates a two-mode entangled NOON state. Such states exhibit greater Wigner negativity than the input, pointing to a route for deterministic non-Gaussian state generation.

What carries the argument

Analytic mapping of input temporal modes to output light via unidirectional scattering on a two-level system, followed by principal-mode decomposition of the two-photon output state.

What would settle it

Compute the overlap or fidelity of the decomposed output state with an ideal two-photon NOON state, or measure the Wigner function of the output to verify whether negativity exceeds that of the single-mode input.

Watch

Extended reading notes

Core claim

By numerically decomposing the output state in terms of its principal modes, we find that it is possible to map single-mode two-photon inputs into two-mode entangled output states, i.e., two-photon NOON states, to very good approximation. The latter states, in turn, are known to have more Wigner negativity compared to the associated input, which ultimately suggests a potential application of our considered setup in the deterministic generation of non-Gaussian states.

Load-bearing premise

The numerical principal-mode decomposition yields a sufficiently accurate approximation to ideal NOON states for the claimed increase in Wigner negativity to be practically useful.

Editorial extensions

If this is right

  • The output approximates ideal NOON states, which carry more Wigner negativity than the single-mode input.
  • This scattering setup offers a deterministic method to generate non-Gaussian quantum states of light without relying on probabilistic sources.
  • The closed-form description in input modes enables direct computation of output properties for arbitrary multimode multiphoton inputs.
  • Temporal mode structure transforms under the scattering in a way that entangles previously unentangled photons across two modes.

Reading between the lines

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

  • The same scattering process might convert other specific input mode combinations into higher-order entangled or non-Gaussian states for larger photon numbers.
  • Experimental tests could focus on preparing well-defined temporal modes and projecting the output onto the identified principal modes to confirm the predicted entanglement.
  • This deterministic mapping could complement existing methods for non-Gaussian state preparation in continuous-variable quantum information processing.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 0 minor

Summary. The manuscript derives an analytic input-output map for the temporal modes of multimode, multiphoton light scattered unidirectionally by a two-level system, expressed explicitly in terms of the input modes. For the special case of two photons in one input mode, numerical principal-mode decomposition of the output is used to argue that the state approximates a two-photon NOON state, which in turn exhibits increased Wigner negativity relative to the input and therefore offers a route to deterministic non-Gaussian state generation.

Significance. The explicit temporal-mode description is a clear technical contribution that improves both interpretability and computational efficiency over purely numerical treatments of the same scattering problem. The numerical observation that a single-mode two-photon input can be mapped to an approximate NOON output would, if properly quantified, constitute a concrete deterministic protocol for enhancing non-Gaussianity; the current lack of fidelity metrics prevents that claim from being evaluated at the level required for practical impact.

major comments (1)
  1. [Abstract] Abstract (and the corresponding numerical results on the two-photon case): the central claim that the output approximates 'two-photon NOON states, to very good approximation' is unsupported by any reported overlap integral, fidelity, trace distance, or other quantitative distance to the ideal state (|2,0⟩ + |0,2⟩)/√2. Because Wigner negativity is a continuous functional, an unquantified approximation leaves open whether the reported negativity increase is large enough to be useful or merely marginal.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We appreciate the acknowledgment of the analytic temporal-mode description as a technical contribution. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the corresponding numerical results on the two-photon case): the central claim that the output approximates 'two-photon NOON states, to very good approximation' is unsupported by any reported overlap integral, fidelity, trace distance, or other quantitative distance to the ideal state (|2,0⟩ + |0,2⟩)/√2. Because Wigner negativity is a continuous functional, an unquantified approximation leaves open whether the reported negativity increase is large enough to be useful or merely marginal.

    Authors: We agree that a quantitative metric is required to substantiate the claim of a 'very good approximation' and to evaluate whether the increase in Wigner negativity is practically meaningful. In the revised manuscript we will report the fidelity (overlap) between the numerically reconstructed output state and the ideal NOON state (|2,0⟩ + |0,2⟩)/√2, computed directly from the principal temporal modes obtained in the decomposition. This addition will allow readers to assess the approximation rigorously. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity detected; analytic scattering map and numerical decomposition are independent

full rationale

The paper derives an explicit analytic input-output map for the scattered light solely in terms of input temporal modes from the two-level system interaction. The two-photon NOON-state approximation is obtained via separate numerical principal-mode decomposition of that output state, without any reduction of the claimed mapping to a fitted parameter, self-definition, or self-citation chain. No equations equate a derived quantity to its own inputs by construction, and the central claim rests on the scattering dynamics rather than renaming or smuggling prior results. This is the normal case of a self-contained derivation.

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

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The two-level system and scattering interaction are treated as standard background.

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0 comments
Cite this review

Pith. "Pith review of Temporal modes of quantum states of light scattered by a two-level system." pith.science (2026). https://pith.science/paper/VRKF6HY7

@misc{pith2026260629974,
  author       = {Pith},
  title        = {Pith review of: Temporal modes of quantum states of light scattered by a two-level system},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VRKF6HY7}},
  note         = {Machine review of arXiv:2606.29974}
}
read the original abstract

Non-Gaussian quantum states of light are of paramount importance to quantum computing. Nevertheless, their deterministic generation is challenging problem due to the difficulty to control nonlinearities in physical systems. In this work, we characterize the light stemming from one of the most fundamental quantum optics configurations: the unidirectional scattering of multimode and multiphoton light by a two-level system. We provide an analytic and explicit description of the output light solely in terms of the corresponding input temporal modes which allows a straightforward physical interpretation and is computationally more effective compared to numerical methods. Then, we focus on the specific case of the scattering of two photons in a single mode. By numerically decomposing the output state in terms of its principal modes, we find that it is possible to map single-mode two-photon inputs to be into two-mode entangled output states, i.e., two-photon NOON states, to very good approximation. The latter states, in turn, are known to have more Wigner negativity compared to the associated input, which ultimately suggests a potential application of our considered setup in the deterministic generation of non-Gaussian states.

Figures

Figures reproduced from arXiv: 2606.29974 by the authors.

Figure 1
Figure 1. FIG. 1: The setup of the considered physical system. A two-level system (TLS), with transition frequency [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Analysis of the modal content of the output [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Different output modes for the Lorentzian input case [see Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Analysis of the modal content of the output [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

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Forward citations

Cited by 1 Pith paper

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Reference graph

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    Hamiltonian and temporal modes The setup of interest consists in a single two-level sys- tem (TLS) coupled to a one-dimensional continuum of photonic modes. The dynamics of the whole system is governed by the HamiltonianHtot =H ph +H at +H int, where Hph = Z ∞ −∞ dk ω ka†(k)a(k),(1) Hat =ω geσee,(2) Hint = r Γ 4π Z ∞ −∞ dk a(k)σ eg +h.c.,(3) are, respecti...

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    are written in units such thatℏ=c= 1, and we as- sume the dispersion relation to beωk =|k|for the photon frequency associated with momentumk. Furthermore, ωge denotes the atomic transition frequency between the excited (|e⟩) and ground (|g⟩) states,σ ee =|e⟩ ⟨e|, σeg =|e⟩ ⟨g|andΓis the spontaneous emission rate of the TLS. The ladder operatorsa†(k),a(k), ...

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    Definition and relation to the output state The scattering matrix (orS-matrix) is an operatorS that maps an input state to a scattered output state, which, in our case, are given by Eqs. (9) and (10), re- spectively. Mathematically, this relation reads [25] |ψout⟩=S |ψ in⟩,(12) and we define the corresponding matrix elements associ- ated with the scatteri...

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    Output mode analysis By plugging Eq. (31) into Eq. (29), we obtain the out- put state’s wavefunction for the Lorentzian input. In this case, the computation can even be performed an- alytically; the explicit expression for the output state wavefunction is given in Appendix C. Then, with the full expression of the output state’s wavefunction, we nu- merica...

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    We recognize inΨout the wavefunction of a Hang-Ou-Mandel state, also known as two-photon NOON state. The principal modesψ1 andψ 2 are plotted in Fig. 3. TheformofEq.(32)furtherimpliesthatonecandefine a rotated basis of modes, as ϕ1(t) = 1√ 2(ψ1(t) +ψ 2(t))(33) ϕ2(t) = 1√ 2(ψ1(t)−ψ 2(t)),(34) such thatϕ1(t)andϕ 2(t)decompose the wavefunction as Ψout(t, t′)...

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