Theory of quantum comb enhanced interferometry

Haowei Shi; Quntao Zhuang

arxiv: 2508.01513 · v2 · pith:HP2JXFAZnew · submitted 2025-08-02 · 🪐 quant-ph · physics.optics

Theory of quantum comb enhanced interferometry

Haowei Shi , Quntao Zhuang This is my paper

Pith reviewed 2026-05-25 08:07 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics

keywords quantum combsdual-comb interferometrysqueezed lightentangled combsquantum sensingloss robustnessstandard quantum limitabsorption spectroscopy

0 comments

The pith

Quantum combs with squeezing and entanglement yield four protocols for dual-comb interferometry with scalable advantages, three of which tolerate loss at isolated lines.

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

The paper develops a theory for quantum frequency combs whose fluctuations are engineered through squeezing and entanglement to surpass the standard quantum limit in dual-comb interferometric measurements. It examines four protocols that pair squeezed or entangled combs with either division receivers or heterodyne receivers. For spectroscopy of a single absorption line, three protocols maintain their quantum advantage despite loss at a few comb lines, and the advantage grows with squeezing or entanglement strength. This form of loss robustness for a scalable advantage has not appeared in conventional quantum sensing protocols.

Core claim

Quantum combs engineered via squeezing and entanglement enable four protocols for dual-comb interferometric measurement that achieve quantum advantages scalable with the squeezing or entanglement strength; in spectroscopy of a single absorption line the division receiver with a squeezed comb suffers entanglement-mismatch noise while the other three protocols remain robust to loss at a few comb lines.

What carries the argument

Quantum frequency comb whose lines carry squeezing or entanglement, combined with division or heterodyne receivers in a dual-comb interferometry setup.

If this is right

Quantum advantages in the four protocols increase directly with squeezing or entanglement strength.
Loss at a few comb lines leaves the advantage intact in three of the protocols.
The division receiver paired with a squeezed comb alone experiences entanglement-mismatch noise amplification.
Heterodyne receivers confer loss robustness for both squeezed and entangled combs.

Where Pith is reading between the lines

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

The loss robustness could support practical dual-comb sensing in environments where only some frequencies suffer attenuation.
The same receiver distinctions might apply to other frequency-comb metrology tasks beyond single-line absorption.
Direct comparison of the four protocols in a single apparatus would test whether the modeled robustness holds under real comb generation.

Load-bearing premise

Squeezing and entanglement can be applied to frequency combs without introducing extra noise sources or receiver imperfections beyond those already modeled.

What would settle it

An experiment that introduces controlled loss to a few comb lines and compares the measured noise levels across the four protocols, checking whether amplified noise appears only in the squeezed-comb division-receiver case.

Figures

Figures reproduced from arXiv: 2508.01513 by Haowei Shi, Quntao Zhuang.

**Figure 1.** Figure 1: Schematic of dual-comb spectroscopy. (a) Heterodyne-receiver-based DCS. The signal comb first probes the sample and then gets combined with the LO comb. (b) Division-receiver-based DCS. The signal comb first gets combined with the LO comb and then probes the sample. We consider two classes of quantum comb engineering: (c) Intra-comb-line squeezing: squeezed pairs are centered around each line; (d) Cross-co… view at source ↗

**Figure 2.** Figure 2: Quantum advantage over classical DCS. We plot SNR advantage (SNR2 in decibel) of quantum GA = GB = 15dB over the corresponding classical limits (GA = GB = 1) of (a) division receiver and (b) heterodyne receiver. The power allocation in both cases is set symmetric as |A| = |B|. M = 1001, total sample exposure P = 15mW, carrier wavelength λ = 1563nm. Acquisition time normalized to T = 1s. of the division rec… view at source ↗

**Figure 3.** Figure 3: Absolute SNR for cross-comb-line entangled combs in DCS. We consider local SNR (Eq. (28)) and global SNR (Eq. (29)) of the division receiver (blue) and the heterodyne detection (red). The power allocation is optimized to maximize SNR in all cases. Quantum gains setup: GA = GB = 15dB with for all, except heterodyne detection in subplot (a) with GA = 15dB, GB = 1. For all the scenarios, we provide the cla… view at source ↗

**Figure 4.** Figure 4: Schematic of the mode definitions. The comb lines are denoted by An, Bn, located at frequency n(ωr + ∆ωr) and nωr respectively, for −N ≤ n ≤ N. For the noise modes Aˆn,m, Bˆn,m, the first subscript n indexes the comb line, while the second subscript m indexes the detuning of the sideband noise mode from the line. To contain all relevant noise modes, −2N ≤ m ≤ 2N. between the two combs. For convenience of o… view at source ↗

**Figure 5.** Figure 5: Two cases of intra-comb-line squeezing. (a) cross-referred squeezing pairs, noises in Aˆ are centered around {Bn} lines while noises in Bˆ are centered around {An} lines, used in heterodyne receiver, and (b) self-referred squeezing pairs, noises centered around {An} for Aˆ and around {Bn} for Bˆ, used in division receiver. at Aˆ n,n, which has an offset with the center of squeezing at Aˆ n,0. In Ref. [14],… view at source ↗

**Figure 6.** Figure 6: Schematic of the mode definitions. The comb lines are denoted by [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

read the original abstract

Optical frequency combs, named for their comb-like peaks in the spectrum, are essential for various sensing applications. As the technology develops, its performance has reached the standard quantum limit dictated by the quantum fluctuations of coherent light field. Quantum combs, with their quantum fluctuation engineered via squeezing and entanglement, are the necessary ingredient for overcoming such limits. We develop the theory for designing and analyzing quantum combs, focusing on dual-comb interferometric measurement. Our analyses cover both squeezed and entangled quantum combs with division receivers and heterodyne receivers, leading to four protocols with quantum advantages scalable with squeezing/entanglement strength. In the spectroscopy of a single absorption line, the division receiver with the squeezed comb suffers from entanglement-mismatching-induced amplified noise, while the other three protocols demonstrate a surprising robustness to loss at a few comb lines. Such a unique loss-robustness of a scalable quantum advantage has not been found in any traditional quantum sensing protocols.

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.

Desk Editor's Note private letter to a colleague

The paper sets out four quantum comb protocols for dual-comb interferometry and claims three retain scalable advantage under partial loss, but the per-line loss model needs checking against possible entanglement cross-talk.

read the letter

Colleague, the main point is that this work develops a theory for quantum combs in dual-comb interferometry and presents four protocols—squeezed-comb heterodyne, entangled-comb division, entangled-comb heterodyne, and squeezed-comb division—where the first three keep a quantum advantage that scales with squeezing or entanglement strength even when loss affects only a few comb lines. They contrast this with the squeezed-comb division case, which picks up extra noise from entanglement mismatch, and note that this kind of loss robustness has not appeared in standard quantum sensing setups. The analysis focuses on spectroscopy of a single absorption line and derives the noise behavior from the quantum states and receiver choices. That framework is the concrete new piece. The paper does a reasonable job separating the protocols by their receiver type and showing where the mismatch arises in one of them. It stays within standard quantum optics tools without obvious circular definitions or fitted parameters. The soft spot is the loss treatment. The robustness rests on modeling loss as independent attenuation on selected lines, with the remaining squeezing or entanglement still delivering advantage. If the entanglement spans the comb, loss on one tooth could mix in vacuum fluctuations across multiple lines in a way the per-line model misses, especially if comb generation or frequency division adds any correlated effects. The stress-test note flags exactly this, and the abstract gives no equations or error analysis to confirm whether those cross terms were included. Without the full derivations it is hard to judge how solid the math is. This is aimed at people working on quantum metrology and frequency-comb sensing who care about loss tolerance. A reader looking for new protocol ideas in that area would get something to think about. It deserves peer review so the derivations and the loss model can be examined in detail.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a theoretical framework for quantum comb enhanced dual-comb interferometry. It analyzes four protocols—squeezed-comb division, squeezed-comb heterodyne, entangled-comb division, and entangled-comb heterodyne—derived from standard quantum optics treatments of squeezing and entanglement across frequency teeth. The central claims are that all four yield scalable quantum advantages with squeezing/entanglement strength, that the squeezed-comb division receiver suffers entanglement-mismatch amplified noise, and that the other three protocols retain their advantage under loss applied to a few comb lines.

Significance. If the derivations and loss model hold, the identification of loss-robust scalable quantum advantage in three protocols would be a meaningful contribution, as the abstract correctly notes that such robustness has not been reported in traditional quantum sensing. The distinction drawn between protocols regarding entanglement mismatch provides a concrete design insight for comb-based sensors.

major comments (2)

[loss analysis section] Loss analysis (around the discussion of per-line attenuation): the robustness claim for the three protocols rests on treating loss as independent attenuation on selected teeth while the remaining squeezing or entanglement continues to suppress noise. It is not shown whether the model incorporates vacuum fluctuations or phase noise that could be mixed across the entangled spectrum by the loss operator itself; if broadband entanglement is present, localized loss can couple additional vacuum modes in a manner not captured by the independent-line treatment. This directly affects whether the reported robustness is an artifact of the loss model.
[protocol definitions] Protocol comparison (division vs. heterodyne receivers): the claim that only the squeezed-comb division receiver experiences entanglement-mismatch noise while the entangled-comb division receiver does not requires an explicit side-by-side calculation of the noise operators after the receiver. Without that, it is unclear whether the distinction follows from the receiver choice or from an implicit assumption about how the comb entanglement is prepared and divided.

minor comments (2)

Notation for comb teeth and loss parameters should be defined once at first use and used consistently; several symbols appear without prior definition in the abstract-level description.
The manuscript would benefit from a table summarizing the four protocols, their receiver type, state type, and whether they exhibit the claimed loss robustness.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the two major comments below and will incorporate clarifications and additional calculations into a revised manuscript.

read point-by-point responses

Referee: [loss analysis section] Loss analysis (around the discussion of per-line attenuation): the robustness claim for the three protocols rests on treating loss as independent attenuation on selected teeth while the remaining squeezing or entanglement continues to suppress noise. It is not shown whether the model incorporates vacuum fluctuations or phase noise that could be mixed across the entangled spectrum by the loss operator itself; if broadband entanglement is present, localized loss can couple additional vacuum modes in a manner not captured by the independent-line treatment. This directly affects whether the reported robustness is an artifact of the loss model.

Authors: Our loss model treats each comb tooth independently via a beam-splitter interaction that mixes the mode with vacuum fluctuations from the loss port, following standard quantum-optics treatments of attenuation. Because the entanglement in the entangled-comb protocols is prepared between discrete, addressable tooth pairs rather than as a single broadband state, loss on a subset of lines introduces vacuum noise only to the affected modes without generating cross-spectral mixing terms beyond those already accounted for in the covariance matrix. Nevertheless, we agree that an expanded derivation of the post-loss noise operators would make this explicit and will add it to the revised manuscript. revision: partial
Referee: [protocol definitions] Protocol comparison (division vs. heterodyne receivers): the claim that only the squeezed-comb division receiver experiences entanglement-mismatch noise while the entangled-comb division receiver does not requires an explicit side-by-side calculation of the noise operators after the receiver. Without that, it is unclear whether the distinction follows from the receiver choice or from an implicit assumption about how the comb entanglement is prepared and divided.

Authors: The distinction originates from the receiver architecture: the squeezed-comb division protocol splits a single squeezed comb, producing a mismatch between the local-oscillator teeth and the signal teeth that amplifies vacuum noise, whereas the entangled-comb division protocol distributes the entangled pairs such that each receiver arm receives a matched entangled tooth. To remove any ambiguity we will insert an explicit side-by-side calculation of the output noise operators for both division receivers in the revised text. revision: yes

Circularity Check

0 steps flagged

No circularity: protocols derived from standard quantum optics without self-referential reductions

full rationale

The abstract and provided context describe four protocols (squeezed-comb heterodyne, entangled-comb division, entangled-comb heterodyne, etc.) analyzed via quantum optics modeling of squeezing, entanglement, division, and heterodyne receivers. Loss robustness is presented as an analyzed outcome under per-line attenuation, not as a fitted parameter renamed as prediction or defined circularly. No self-citation load-bearing steps, uniqueness theorems imported from authors, or ansatzes smuggled via citation are evident in the text. The derivation chain remains self-contained against external quantum optics benchmarks, with the uniqueness claim framed as an empirical finding rather than a definitional tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the theory relies on standard quantum optics for comb engineering but introduces new protocol combinations whose assumptions are not detailed here.

axioms (1)

domain assumption Quantum fluctuations in frequency combs can be engineered via squeezing and entanglement without additional unmodeled noise.
Central to the four protocols and their claimed advantages.

pith-pipeline@v0.9.0 · 5682 in / 1146 out tokens · 30836 ms · 2026-05-25T08:07:13.526042+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

G′_X ≡ ½(G_X + 1/G_X) ... amplified spontaneous emission noises
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

four protocols ... loss-robustness of a scalable quantum advantage

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Quantum optics of frequency comb metrology
quant-ph 2026-05 conditional novelty 7.0

A quantum-optical theory for frequency combs based on continuous-mode quantization reveals a spectral-envelope dependence in the optical frequency division limit and a cyclostationary noise penalty in dual-comb spectroscopy.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · cited by 1 Pith paper

[1]

T. W. Hänsch, Nobel lecture: Passion for precision, Rev. Mod. Phys.78, 1297 (2006)

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J.L.Hall,Nobellecture: Definingandmeasuringoptical frequencies, Rev. Mod. Phys.78, 1279 (2006)

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Picqué and T

N. Picqué and T. W. Hänsch, Frequency comb spec- troscopy, Nature Photonics13, 146 (2019)

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Coddington, N

I. Coddington, N. Newbury, and W. Swann, Dual-comb spectroscopy, Optica3, 414 (2016)

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T. Fortier and E. Baumann, 20 years of developments in optical frequency comb technology and applications, Communications Physics2, 153 (2019)

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P. Martín-Mateos, F. U. Khan, and O. E. Bonilla- Manrique, Direct hyperspectral dual-comb imaging, Op- tica 7, 199 (2020)

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Vicentini, Z

E. Vicentini, Z. Wang, K. Van Gasse, T. W. Hänsch, and N. Picqué, Dual-comb hyperspectral digital holography, Nature Photonics15, 890 (2021)

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I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, Rapid and precise absolute distance measure- ments at long range, Nature Photonics3, 351 (2009)

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Lukashchuk, J

A. Lukashchuk, J. Riemensberger, M. Karpov, J. Liu, and T. J. Kippenberg, Dual chirped microcomb based parallel ranging at megapixel-line rates, Nature Com- munications 13, 3280 (2022)

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M.-G. Suh and K. J. Vahala, Soliton microcomb range measurement, Science359, 884 (2018)

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E. D. Caldwell, L. C. Sinclair, N. R. Newbury, and J.- D. Deschenes, The time-programmable frequency comb and its use in quantum-limited ranging, Nature610, 667 (2022)

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H. Shi, Z. Chen, S. E. Fraser, M. Yu, Z. Zhang, and Q. Zhuang, Entanglement-enhanced dual-comb spec- troscopy, npj Quantum Information9, 91 (2023)

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[14]

D. I. Herman, M. Walsh, M. K. Kreider, N. Lordi, E. J. Tsao, A. J. Lind, M. Heyrich, J. Combes, J. Genest, and S. A. Diddams, Squeezed dual-comb spectroscopy, Science 387, 653 (2025)

work page 2025
[15]

Hariri, S

A. Hariri, S. Liu, H. Shi, Q. Zhuang, X. Fan, and Z. Zhang, Entangled dual-comb spectroscopy, arXiv:2412.19800 (2024)

work page arXiv 2024
[16]

Demkowicz-Dobrzański, K

R. Demkowicz-Dobrzański, K. Banaszek, and R. Schn- abel, Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational wave detector geo 600, Physical Review A—Atomic, Molecular, and Optical Physics88, 041802 (2013)

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[17]

Frascella, S

G. Frascella, S. Agne, F. Y. Khalili, and M. V. Chekhova, Overcoming detection loss and noise in squeezing-based optical sensing, npj Quantum Informa- tion 7, 72 (2021)

work page 2021
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C. A. Casacio, L. S. Madsen, A. Terrasson, M. Waleed, K. Barnscheidt, B. Hage, M. A. Taylor, and W. P. Bowen, Quantum-enhanced nonlinear microscopy, Na- ture 594, 201 (2021)

work page 2021
[19]

Weedbrook, S

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Reviews of Modern Physics84, 621 (2012). 10 CONTENTS References 9 A. Theory framework 10 B. Combine then pass through sample 12

work page 2012
[20]

intra-comb-line squeezing 13 b

Division data processing 13 a. intra-comb-line squeezing 13 b. cross-comb-line entanglement 14

work page
[21]

Pass through sample and then interfere 17

Subtraction data processing 17 C. Pass through sample and then interfere 17

work page
[22]

Division data processing 18

work page
[23]

Intra-comb-line squeezing 18 b

Subtraction data processing 18 a. Intra-comb-line squeezing 18 b. Cross comb line entanglement 19 Appendix A: Theory framework To describe the field, we use the field annihilation op- erator ˆA, which satisfies the commutation relation [ ˆA(ω), ˆA†(ω′)] = 2πδ (ω − ω′) , (A1) in spectral domain, and [ ˆA(t), ˆA†(t′)] = δ (t − t′) , (A2) in time domain. The...

work page
[24]

Division data processing From Eqs. (B7), we can extract information about the absorption κm and κ−m by measuring the ratio of the mean photocurrent spectra − D ˆIA(m∆ωr) E D ˆIB(m∆ωr) E ≡ rm = c+,mκm + c−,mκ−m (B15) where c+,m = AmB⋆ m/(AmB⋆ m + A⋆ −mB−m) and c−,m = A⋆ −mB−m/(AmB⋆ m + A⋆ −mB−m) are O(1) parameters. For example, for symmetric comb An = A∗ ...

work page
[25]

(B7), it appears that a subtraction between the two photocurrents, in analogy to a balanced homo- dyne receiver, also yields information about the absorp- tion spectrum

Subtraction data processing From Eq. (B7), it appears that a subtraction between the two photocurrents, in analogy to a balanced homo- dyne receiver, also yields information about the absorp- tion spectrum. However, different from homodyne, hereD ˆIB(m∆ωr) E does not carry any information about the sample, sosubtractiononlyinvokesanextraunnecessary loss w...

work page
[26]

In this sense, we only analyze the subtraction data processing

Division data processing From the calculation of mean values, it is immediately clear that division data processing, which measures the ratio ˆIA(m∆ωr)/ˆIB(m∆ωr), does not provide any in- formation about the absorption spectrum{κm} to the leading order, because the ratio of the mean values is a constant −1 independent on {κm}. In this sense, we only analy...

work page
[27]

(C8) Its mean value is D ˆdm E = √κmeiθn AmB⋆ m+√κ−me−iθn A⋆ −mB−m

Subtraction data processing Subtraction data processing measures the differential photocurrent spectrum ˆdm = ˆIA(m∆ωr) − ˆIB(m∆ωr). (C8) Its mean value is D ˆdm E = √κmeiθn AmB⋆ m+√κ−me−iθn A⋆ −mB−m. (C9) The variance is var(ˆdm) = var[∆ˆIA(m∆ωr) − ∆ˆIB(m∆ωr)] . (C10) From Eq. (28) of the main text, the SNR for the esti- mation of √κm is given by|AmB⋆ m|...

work page

[1] [1]

T. W. Hänsch, Nobel lecture: Passion for precision, Rev. Mod. Phys.78, 1297 (2006)

work page 2006

[2] [2]

J.L.Hall,Nobellecture: Definingandmeasuringoptical frequencies, Rev. Mod. Phys.78, 1279 (2006)

work page 2006

[3] [3]

Picqué and T

N. Picqué and T. W. Hänsch, Frequency comb spec- troscopy, Nature Photonics13, 146 (2019)

work page 2019

[4] [4]

Coddington, N

I. Coddington, N. Newbury, and W. Swann, Dual-comb spectroscopy, Optica3, 414 (2016)

work page 2016

[5] [5]

Fortier and E

T. Fortier and E. Baumann, 20 years of developments in optical frequency comb technology and applications, Communications Physics2, 153 (2019)

work page 2019

[6] [6]

Martín-Mateos, F

P. Martín-Mateos, F. U. Khan, and O. E. Bonilla- Manrique, Direct hyperspectral dual-comb imaging, Op- tica 7, 199 (2020)

work page 2020

[7] [7]

Vicentini, Z

E. Vicentini, Z. Wang, K. Van Gasse, T. W. Hänsch, and N. Picqué, Dual-comb hyperspectral digital holography, Nature Photonics15, 890 (2021)

work page 2021

[8] [8]

Coddington, W

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, Rapid and precise absolute distance measure- ments at long range, Nature Photonics3, 351 (2009)

work page 2009

[9] [9]

Trocha, M

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, Ultrafast optical ranging using microres- onatorsolitonfrequencycombs,Science 359,887(2018)

work page 2018

[10] [10]

Lukashchuk, J

A. Lukashchuk, J. Riemensberger, M. Karpov, J. Liu, and T. J. Kippenberg, Dual chirped microcomb based parallel ranging at megapixel-line rates, Nature Com- munications 13, 3280 (2022)

work page 2022

[11] [11]

Suh and K

M.-G. Suh and K. J. Vahala, Soliton microcomb range measurement, Science359, 884 (2018)

work page 2018

[12] [12]

E. D. Caldwell, L. C. Sinclair, N. R. Newbury, and J.- D. Deschenes, The time-programmable frequency comb and its use in quantum-limited ranging, Nature610, 667 (2022)

work page 2022

[13] [13]

H. Shi, Z. Chen, S. E. Fraser, M. Yu, Z. Zhang, and Q. Zhuang, Entanglement-enhanced dual-comb spec- troscopy, npj Quantum Information9, 91 (2023)

work page 2023

[14] [14]

D. I. Herman, M. Walsh, M. K. Kreider, N. Lordi, E. J. Tsao, A. J. Lind, M. Heyrich, J. Combes, J. Genest, and S. A. Diddams, Squeezed dual-comb spectroscopy, Science 387, 653 (2025)

work page 2025

[15] [15]

Hariri, S

A. Hariri, S. Liu, H. Shi, Q. Zhuang, X. Fan, and Z. Zhang, Entangled dual-comb spectroscopy, arXiv:2412.19800 (2024)

work page arXiv 2024

[16] [16]

Demkowicz-Dobrzański, K

R. Demkowicz-Dobrzański, K. Banaszek, and R. Schn- abel, Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational wave detector geo 600, Physical Review A—Atomic, Molecular, and Optical Physics88, 041802 (2013)

work page 2013

[17] [17]

Frascella, S

G. Frascella, S. Agne, F. Y. Khalili, and M. V. Chekhova, Overcoming detection loss and noise in squeezing-based optical sensing, npj Quantum Informa- tion 7, 72 (2021)

work page 2021

[18] [18]

C. A. Casacio, L. S. Madsen, A. Terrasson, M. Waleed, K. Barnscheidt, B. Hage, M. A. Taylor, and W. P. Bowen, Quantum-enhanced nonlinear microscopy, Na- ture 594, 201 (2021)

work page 2021

[19] [19]

Weedbrook, S

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Reviews of Modern Physics84, 621 (2012). 10 CONTENTS References 9 A. Theory framework 10 B. Combine then pass through sample 12

work page 2012

[20] [20]

intra-comb-line squeezing 13 b

Division data processing 13 a. intra-comb-line squeezing 13 b. cross-comb-line entanglement 14

work page

[21] [21]

Pass through sample and then interfere 17

Subtraction data processing 17 C. Pass through sample and then interfere 17

work page

[22] [22]

Division data processing 18

work page

[23] [23]

Intra-comb-line squeezing 18 b

Subtraction data processing 18 a. Intra-comb-line squeezing 18 b. Cross comb line entanglement 19 Appendix A: Theory framework To describe the field, we use the field annihilation op- erator ˆA, which satisfies the commutation relation [ ˆA(ω), ˆA†(ω′)] = 2πδ (ω − ω′) , (A1) in spectral domain, and [ ˆA(t), ˆA†(t′)] = δ (t − t′) , (A2) in time domain. The...

work page

[24] [24]

Division data processing From Eqs. (B7), we can extract information about the absorption κm and κ−m by measuring the ratio of the mean photocurrent spectra − D ˆIA(m∆ωr) E D ˆIB(m∆ωr) E ≡ rm = c+,mκm + c−,mκ−m (B15) where c+,m = AmB⋆ m/(AmB⋆ m + A⋆ −mB−m) and c−,m = A⋆ −mB−m/(AmB⋆ m + A⋆ −mB−m) are O(1) parameters. For example, for symmetric comb An = A∗ ...

work page

[25] [25]

(B7), it appears that a subtraction between the two photocurrents, in analogy to a balanced homo- dyne receiver, also yields information about the absorp- tion spectrum

Subtraction data processing From Eq. (B7), it appears that a subtraction between the two photocurrents, in analogy to a balanced homo- dyne receiver, also yields information about the absorp- tion spectrum. However, different from homodyne, hereD ˆIB(m∆ωr) E does not carry any information about the sample, sosubtractiononlyinvokesanextraunnecessary loss w...

work page

[26] [26]

In this sense, we only analyze the subtraction data processing

Division data processing From the calculation of mean values, it is immediately clear that division data processing, which measures the ratio ˆIA(m∆ωr)/ˆIB(m∆ωr), does not provide any in- formation about the absorption spectrum{κm} to the leading order, because the ratio of the mean values is a constant −1 independent on {κm}. In this sense, we only analy...

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[27] [27]

(C8) Its mean value is D ˆdm E = √κmeiθn AmB⋆ m+√κ−me−iθn A⋆ −mB−m

Subtraction data processing Subtraction data processing measures the differential photocurrent spectrum ˆdm = ˆIA(m∆ωr) − ˆIB(m∆ωr). (C8) Its mean value is D ˆdm E = √κmeiθn AmB⋆ m+√κ−me−iθn A⋆ −mB−m. (C9) The variance is var(ˆdm) = var[∆ˆIA(m∆ωr) − ∆ˆIB(m∆ωr)] . (C10) From Eq. (28) of the main text, the SNR for the esti- mation of √κm is given by|AmB⋆ m|...

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