pith. sign in

arxiv: 2605.16135 · v1 · pith:XDODJIGNnew · submitted 2026-05-15 · 🪐 quant-ph · physics.optics

Sub-picosecond inter-core skew characterization in multicore fibers via Hong--Ou--Mandel interference

L. Lira Tacca , L. Marques Fagundes , M. Morales Lillo , M. Navarro , I. Machuca , S. G\'omez , G. H. dos Santos , J. Cari\~ne
show 4 more authors
G. Saavedra E. S. G\'omez G. Lima S. P. Walborn
This is my paper

Pith reviewed 2026-05-20 18:19 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics
keywords multicore fiberinter-core skewHong-Ou-Mandel interferencedifferential group delayspace division multiplexingquantum photonicstiming measurement
0
0 comments X

The pith

Hong-Ou-Mandel interference measures inter-core skew in multicore fibers with 0.11 picosecond precision.

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

This paper establishes a method to measure inter-core skew, the timing difference between light paths in separate cores of a multicore fiber, using two-photon interference. Accurate knowledge of these delays is essential for synchronizing signals in space-division multiplexed systems and quantum networks. The approach integrates a 4x4 beam splitter made from the fiber itself and records the shift in Hong-Ou-Mandel interference patterns for every core pair. Centers of the interference features give the skew values directly. The measurements reveal that skew grows with the square root of length, as expected for random variations along the fiber, and achieve a precision far beyond conventional techniques.

Core claim

By extracting the center position of HOM interference dips and peaks across all twelve core-pair combinations, individual ICS values are obtained with a demonstrated precision of ±0.11 ps. The root-mean-square ICS grows as σ_τ(L) = κ√L + c with κ = 48.7 ± 2.5 ps/√km and c = 9.76 ± 1.2 ps over lengths from 7.7 m to 1300 m. This provides the first direct validation of stochastic random-walk scaling for installed fibers, enabled by the method's immunity to first-order path fluctuations.

What carries the argument

Hong-Ou-Mandel interference feature positions in a fiber-integrated 4×4 multiport beam splitter that encode pairwise differential group delays between cores.

If this is right

  • ICS values for every core pair are extracted with ±0.11 ps precision limited only by delay stage accuracy.
  • The root-mean-square skew follows a square-root length dependence plus offset across more than two orders of magnitude in length.
  • HOM interference allows characterization of long installed fibers where classical interferometry fails due to path fluctuations.
  • The precision is approximately 180 times better than that of correlation OTDR.
  • Analysis shows a fundamental precision limit in the femtosecond regime with improved delay control.

Where Pith is reading between the lines

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

  • This technique may allow real-time monitoring of timing uniformity in deployed multicore fiber networks for quantum key distribution.
  • Similar interference methods could be adapted to characterize skew in other multi-core or multi-mode systems beyond the current four-core fiber.
  • Reaching the predicted femtosecond precision would enable new applications in high-rate quantum repeaters using space-division multiplexing.

Load-bearing premise

The observed positions of the HOM interference dips and peaks are determined solely by the differential group delay between cores without meaningful contributions from higher-order dispersion or polarization effects.

What would settle it

An independent measurement of inter-core skew on the same fiber samples using a calibrated high-resolution time-of-flight technique that yields values differing by more than the stated uncertainty of 0.11 ps.

Figures

Figures reproduced from arXiv: 2605.16135 by E. S. G\'omez, G. H. dos Santos, G. Lima, G. Saavedra, I. Machuca, J. Cari\~ne, L. Lira Tacca, L. Marques Fagundes, M. Morales Lillo, M. Navarro, S. G\'omez, S. P. Walborn.

Figure 1
Figure 1. Figure 1: Illustration of ICS accumulation in a MCF. Identical pulses propagate (here [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: a) Experimental setup for HOM interference using SPDC source. The photons [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: HOM interference data. (a) Normalised coincidence counts for all six output [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Scaling of the ICSRMS as a function of fiber length 𝐿 in log-log scale for all measured lengths 𝐿. Experimental measurements (markers with error bars) are fitted using Eq. (4) (dot-dashed pink line) and a weighted power-law model ICS ∝ 𝐿 𝛼 (solid blue line). The shaded region represents the propagated uncertainty of the fit in log space. Reference scalings 𝐿 0.5 (dashed red) and 𝐿 1 (dotted black) are show… view at source ↗
read the original abstract

Inter-core skew (ICS), the differential group delay between cores of a multicore fiber (MCF), is a critical parameter for both classical space-division multiplexed communications and quantum photonic networks. We present a high-precision measurement of ICS in a commercially available four-core fiber using two-photon Hong--Ou--Mandel (HOM) interference in a fiber-integrated $4\times4$ multiport beam splitter. By extracting the center position of HOM interference dips and peaks across all twelve core-pair combinations, we obtain individual ICS values with a demonstrated precision of $\pm0.11\,$ps, limited by the delay-stage positioning uncertainty. The root-mean-square ICS grows as $\sigma_\tau(L) = \kappa\sqrt{L}+c$ with $\kappa = 48.7 \pm 2.5\,\mathrm{ps}/\!\sqrt{\mathrm{km}}$ and $c = 9.76 \pm 1.2\,$ps, over fiber lengths from $7.7\,$m to $1300\,$m. This first direct validation of the stochastic random-walk scaling across a length range spanning laboratory to field-deployed scales was made possible by HOM's immunity to first-order path fluctuations, which renders classical interferometric methods impractical for long installed fibers. The demonstrated $\pm0.11\,$ps precision represents a $\sim\!180$-fold improvement over correlation optical time-domain reflectometry (C-OTDR), the standard method for long-fiber ICS characterization. Fisher information analysis establishes a fundamental Cram\'er--Rao precision limit in the femtosecond range, indicating further improvement is achievable with better delay control. These results establish a practical platform for characterising timing uniformity in MCF-based networks for both quantum and classical space-division multiplexed applications.

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 / 2 minor

Summary. The manuscript presents an experimental method to characterize inter-core skew (ICS) in a commercially available four-core multicore fiber using Hong-Ou-Mandel (HOM) interference within a fiber-integrated 4×4 multiport beam splitter. By locating the centers of HOM dips and peaks for all twelve core-pair combinations, the authors extract individual ICS values with a reported precision of ±0.11 ps, limited by delay-stage positioning uncertainty. They further report that the root-mean-square ICS scales as σ_τ(L) = κ√L + c over fiber lengths from 7.7 m to 1300 m, with fitted values κ = 48.7 ± 2.5 ps/√km and c = 9.76 ± 1.2 ps. The approach is positioned as enabling high-precision measurements on long installed fibers due to immunity to first-order path fluctuations, achieving an approximately 180-fold improvement over correlation optical time-domain reflectometry (C-OTDR), with supporting Fisher information analysis indicating potential for femtosecond-level precision.

Significance. If the central extraction of ICS from HOM feature centers is free of significant unaccounted systematics, this work provides a valuable high-precision tool for timing characterization in multicore fibers relevant to both quantum photonic networks and classical space-division multiplexing. The direct experimental validation of the stochastic random-walk scaling model across laboratory to field-deployed length scales is a notable strength, as is the demonstration of a practical platform that overcomes limitations of classical interferometry on long fibers. The quantitative improvement over C-OTDR and the Cramér-Rao bound analysis add to the practical impact for network design and deployment.

major comments (1)
  1. [Abstract] Abstract and data-extraction description: the claim that the demonstrated precision of ±0.11 ps is limited solely by delay-stage positioning uncertainty rests on the assumption that HOM dip/peak centers directly and exclusively report differential group delay. No explicit analysis, simulation, or experimental check is provided for possible net offsets arising from core-to-core differences in higher-order dispersion (β2), birefringence, or residual multiport imperfections, which could accumulate over the 7.7 m–1300 m length range and bias both the individual ICS values and the fitted scaling parameters κ and c. This assumption is load-bearing for the precision and improvement-factor claims.
minor comments (2)
  1. [Abstract] Abstract: the Fisher information analysis establishing the femtosecond-range Cramér-Rao limit is mentioned but not located or summarized in the provided text; a brief pointer to the relevant section or equation would improve clarity.
  2. Notation: ensure consistent formatting of units (e.g., ps/√km) and symbols (κ, c) between the abstract, main text, and any tables or figures reporting the fit results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The major comment identifies a key assumption in our precision claims, which we address point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and data-extraction description: the claim that the demonstrated precision of ±0.11 ps is limited solely by delay-stage positioning uncertainty rests on the assumption that HOM dip/peak centers directly and exclusively report differential group delay. No explicit analysis, simulation, or experimental check is provided for possible net offsets arising from core-to-core differences in higher-order dispersion (β2), birefringence, or residual multiport imperfections, which could accumulate over the 7.7 m–1300 m length range and bias both the individual ICS values and the fitted scaling parameters κ and c. This assumption is load-bearing for the precision and improvement-factor claims.

    Authors: We agree that the manuscript does not contain an explicit analysis, simulation, or experimental verification of possible systematic offsets from core-to-core β2 differences, birefringence, or residual multiport imperfections. This is a substantive point, as such effects could in principle introduce length-dependent biases. However, the center position of the HOM dip or peak is set by the first-order group-delay difference; for a symmetric source spectrum, higher-order dispersion terms primarily broaden the feature or reduce visibility without shifting its center. Birefringence contributions are suppressed by the polarization controllers in the setup, and the 4×4 multiport is a commercial device with specified low port imbalance. The observed consistency of the random-walk scaling over more than two orders of magnitude in length further suggests that any accumulating bias is small compared with the reported precision. To strengthen the presentation, the revised manuscript will add a supplementary section containing order-of-magnitude estimates and simple numerical simulations (using typical fiber parameters) showing that these systematics contribute <0.03 ps to the extracted ICS values—well below the ±0.11 ps level set by delay-stage uncertainty. The abstract and methods will be updated to state the assumption explicitly together with this supporting analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central ICS extraction is direct experimental measurement

full rationale

The paper's load-bearing claim extracts ICS values directly from measured center positions of HOM interference features across core pairs, with precision stated as limited by independent delay-stage uncertainty. This is an empirical observation, not a derivation that reduces to fitted parameters or self-citations by construction. The subsequent empirical scaling fit σ_τ(L) = κ√L + c is presented as a secondary characterization result over measured lengths, not as a first-principles prediction or load-bearing element. No self-definitional loops, fitted inputs renamed as predictions, or uniqueness theorems imported from prior self-work appear in the provided derivation chain. The method is self-contained against external benchmarks via direct two-photon interference data.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The measurement relies on the standard quantum optics model of HOM interference and the assumption that the fiber cores behave as independent waveguides with stochastic length variations; two parameters are fitted to the length-dependent data.

free parameters (2)
  • κ = 48.7 ps/√km
    Slope of the random-walk scaling for RMS ICS, fitted to measured data across multiple lengths.
  • c = 9.76 ps
    Constant offset term in the RMS ICS scaling law, fitted to the same dataset.
axioms (1)
  • domain assumption The center of the HOM dip or peak directly encodes the differential group delay between the two cores under test.
    Invoked when converting interference feature positions to individual ICS values for each core pair.

pith-pipeline@v0.9.0 · 5924 in / 1418 out tokens · 61982 ms · 2026-05-20T18:19:39.007372+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

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

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.

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages

  1. [1]

    Space-division multiplexing in optical fibres,

    D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics7, 354–362 (2013)

    work page 2013

  2. [2]

    Multicore fiber technology,

    K. Saitoh and S. Matsuo, “Multicore fiber technology,” J. Light. Technol.34, 55–66 (2016)

    work page 2016

  3. [3]

    102petabit/stransmissionover1,808.1kmina19-corerandomly-coupled multicore fiber,

    R.S.Luis,M.v.d.Hout,S.Gaiani,etal.,“102petabit/stransmissionover1,808.1kmina19-corerandomly-coupled multicore fiber,” inOptical Fiber Communication Conference (OFC) Postdeadline Papers 2025,(Optica Publishing Group, 2025), p. Th4A.1

    work page 2025

  4. [4]

    On the performance of joint-core carrier-phase estimation in the presence of intercore skew,

    A. F. Alfredsson, E. Agrell, M. Karlsson, and H. Wymeersch, “On the performance of joint-core carrier-phase estimation in the presence of intercore skew,” J. Light. Technol.37, 5291–5298 (2019)

    work page 2019

  5. [5]

    On the impact of inter-core skew on multiple-span coupled-core MCF transmissions,

    J. Cai, D. Hu, W. Wang,et al., “On the impact of inter-core skew on multiple-span coupled-core MCF transmissions,” in2024 Asia Communications and Photonics Conference (ACP) and International Conference on Information Photonics and Optical Communications (IPOC),(IEEE, 2024), pp. 1–4

    work page 2024

  6. [6]

    Demonstration of uncoupled 4-core multicore fiber in submarine cable prototype with integrated multicore edfa,

    H. Takeshita, K. Nakamura, Y. Matsuo,et al., “Demonstration of uncoupled 4-core multicore fiber in submarine cable prototype with integrated multicore edfa,” J. Light. Technol.41, 980–988 (2023)

    work page 2023

  7. [7]

    High-capacity optical communication relayed by multi-core amplifier on deployed submarine seven-core fiber cable,

    Y. Chen, J. Zhou, Y. Wu,et al., “High-capacity optical communication relayed by multi-core amplifier on deployed submarine seven-core fiber cable,” Commun. Eng. (2026)

    work page 2026

  8. [8]

    Advancements in key technological building blocks for enabling mcf implementation,

    T. Nakanishi, T. Hayashi, S. Mouri, and T. Hasegawa, “Advancements in key technological building blocks for enabling mcf implementation,” inOptical Fiber Communication Conference (OFC) 2024,(Optica Publishing Group, 2024), p. W4J.1

    work page 2024

  9. [9]

    Multidimensional entanglement generation with multicore optical fibers,

    E. Gómez, S. Gómez, I. Machuca,et al., “Multidimensional entanglement generation with multicore optical fibers,” Phys. Rev. Appl.15, 034024 (2021)

    work page 2021

  10. [10]

    Experimental space-division multiplexed polarization-entanglement distribution through 12 paths of a multicore fiber,

    E. A. Ortega, K. Dovzhik, J. Fuenzalida,et al., “Experimental space-division multiplexed polarization-entanglement distribution through 12 paths of a multicore fiber,” PRX Quantum2, 040356 (2021)

    work page 2021

  11. [11]

    High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,

    G. Cañas, N. Vera, J. Cariñe,et al., “High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers,” Phys. Rev. A96, 022317 (2017)

    work page 2017

  12. [12]

    Quantum key distribution over multicore fiber,

    J. F. Dynes, S. J. Kindness, S. W.-B. Tam,et al., “Quantum key distribution over multicore fiber,” Opt. Express24, 8081–8087 (2016)

    work page 2016

  13. [13]

    Quantum information processing with space-division multiplexing optical fibres,

    G. B. Xavier and G. Lima, “Quantum information processing with space-division multiplexing optical fibres,” Commun. Phys.3, 9 (2020)

    work page 2020

  14. [14]

    Multi-core fiber integrated multi-port beam splitters for quantum information processing,

    J. Cariñe, G. Cañas, P. Skrzypczyk,et al., “Multi-core fiber integrated multi-port beam splitters for quantum information processing,” Optica7, 542–550 (2020)

    work page 2020

  15. [15]

    Sub-femtosecond stabilization of multicore fiber for high-fidelity quantum networking at 100% duty cycle,

    T. Nakamura, N. Hoghooghi, N. Fontaine,et al., “Sub-femtosecond stabilization of multicore fiber for high-fidelity quantum networking at 100% duty cycle,” APL Photonics11, 026113 (2026)

    work page 2026

  16. [16]

    Azimuth-rotated splicings of a four-core optical fiber for inter-core group delay compensation,

    H. J. Lee, E. Lee, and H. S. Park, “Azimuth-rotated splicings of a four-core optical fiber for inter-core group delay compensation,” IEEE Photonics Technol. Lett.29, 2250–2253 (2017). Demonstrates that rotated-splice ICS compensation is incomplete, providing evidence for the stochastic random-walk character of ICS

    work page 2017

  17. [17]

    Group delay measurements of multicore fibers with correlation optical time domain reflectometry,

    F. Azendorf, A. Dochhan, F. Spinty,et al., “Group delay measurements of multicore fibers with correlation optical time domain reflectometry,” in2020 22nd International Conference on Transparent Optical Networks (ICTON), (IEEE, 2020), pp. 1–4

    work page 2020

  18. [18]

    Measurement of differential mode group delay in few-mode fiber with correlation optical time-domain reflectometer,

    L. Jin, Y. Wang, M. Zhang,et al., “Measurement of differential mode group delay in few-mode fiber with correlation optical time-domain reflectometer,” Appl. Opt.61, 3579–3582 (2022)

    work page 2022

  19. [19]

    Multi-core fiber interferometer using spatial light modulators for measurement of the inter-core group index differences,

    H. J. Lee, H. S. Moon, S.-K. Choi, and H. S. Park, “Multi-core fiber interferometer using spatial light modulators for measurement of the inter-core group index differences,” Opt. Express23, 12555–12561 (2015)

    work page 2015

  20. [20]

    Measurement of subpicosecond time intervals between two photons by interference,

    C.-K. Hong, Z.-Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett.59, 2044 (1987)

    work page 2044

  21. [21]

    Robust interferometric sensing using two-photon interference,

    G. H. Aguilar, R. S. Piera, P. L. Saldanha,et al., “Robust interferometric sensing using two-photon interference,” Phys. Rev. Appl.14, 024028 (2020)

    work page 2020

  22. [22]

    High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,

    P. Aboussouan, O. Alibart, D. B. Ostrowsky,et al., “High-visibility two-photon interference at a telecom wavelength using picosecond-regime separated sources,” Phys. Rev. A81, 021801 (2010)

    work page 2010

  23. [23]

    Spectral correlation measurements at the Hong–Ou–Mandel interference dip,

    T. Gerrits, F. Marsili, V. B. Verma,et al., “Spectral correlation measurements at the Hong–Ou–Mandel interference dip,” Phys. Rev. A91, 013830 (2015)

    work page 2015

  24. [24]

    Characteristics of homogeneous multi-core fibers for SDM transmission,

    B. J. Puttnam, R. S. Luís, G. Rademacher,et al., “Characteristics of homogeneous multi-core fibers for SDM transmission,” APL Photonics4, 022804 (2019)

    work page 2019

  25. [25]

    B. E. A. Saleh and M. C. Teich,Fundamentals of Photonics(Wiley, Hoboken, NJ, 2019), 3rd ed

    work page 2019

  26. [26]

    Phenomenological approach to polarisation dispersion in long single-mode fibres,

    C. D. Poole and R. E. Wagner, “Phenomenological approach to polarisation dispersion in long single-mode fibres,” Electron. Lett.22, 1029–1030 (1986)

    work page 1986

  27. [27]

    Statistical treatment of polarization dispersion in single-mode fiber,

    C. D. Poole, “Statistical treatment of polarization dispersion in single-mode fiber,” Opt. Lett.13, 687–689 (1988)

    work page 1988

  28. [28]

    Quantum metrology timing limits of the Hong–Ou–Mandel interferometer and of general two-photon measurements,

    K. M. Jordan, R. A. Abrahao, and J. S. Lundeen, “Quantum metrology timing limits of the Hong–Ou–Mandel interferometer and of general two-photon measurements,” Phys. Rev. A106, 063715 (2022)

    work page 2022

  29. [29]

    S. M. Kay,Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory(Prentice Hall, Englewood Cliffs, NJ, 1993)

    work page 1993

  30. [30]

    SM-4C1500(8.0/125)/001 four-core single-mode fiber datasheet,

    Fibercore (Humanetics Group), “SM-4C1500(8.0/125)/001 four-core single-mode fiber datasheet,” https://fibercore. humaneticsgroup.com/products/multicore-fiber/multicore-fiber/sm-4c150080125001 (2024). Operating wavelength 1520–1650nm; 4-core square arrangement; 50𝜇m core spacing; 125𝜇m cladding

    work page 2024

  31. [31]

    Maximizing quantum discord from interference in multi-port fiber beamsplitters,

    J. Cariñe, M. N. Asan-Srain, G. Lima, and S. P. Walborn, “Maximizing quantum discord from interference in multi-port fiber beamsplitters,” npj Quantum Inf.7, 172 (2021)

    work page 2021

  32. [32]

    Inter-core skew measurements in temperature controlled multi-core fiber,

    B. J. Puttnam, G. Rademacher, R. S. Luis,et al., “Inter-core skew measurements in temperature controlled multi-core fiber,” inOptical Fiber Communication Conference,(Optica Publishing Group, 2018), pp. Tu3B–3

    work page 2018

  33. [33]

    Impact of temperature on propagation time and inter-core skew in a 19-core fiber,

    B. J. Puttnam, G. Rademacher, R. S. Luís,et al., “Impact of temperature on propagation time and inter-core skew in a 19-core fiber,” inAsia Communications and Photonics Conference,(Optica Publishing Group, 2018), pp. S3K–4

    work page 2018