pith. sign in

arxiv: 2504.07030 · v2 · submitted 2025-04-09 · 🪐 quant-ph · hep-ex· hep-ph

Decoherence effects in entangled fermion pairs at colliders

Rafael Aoude , Alan J. Barr , Fabio Maltoni , Leonardo Satrioni This is my paper

Pith reviewed 2026-05-22 19:45 UTC · model grok-4.3

classification 🪐 quant-ph hep-exhep-ph
keywords entanglementdecoherencefermion pairscollidersKraus operatorsAltarelli-ParisiBell stateradiation effects
0
0 comments X

The pith

Radiation decoherence in entangled top-quark pairs at colliders is captured by mapping Kraus operators to integrated Altarelli-Parisi splitting functions.

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

The paper calculates how radiation causes loss of spin entanglement in maximally entangled fermion pairs produced at colliders. It treats the pair as an open quantum system in a Bell state and shows that the evolution operators can be identified with the integrated Altarelli-Parisi splitting functions that describe parton radiation. A sympathetic reader cares because recent LHC measurements have reported spin entanglement in top-antitop pairs, yet those analyses usually omit the radiation that is expected to reduce the observed entanglement. If the identification holds, collider experiments can incorporate a concrete, calculable correction for decoherence instead of ignoring it.

Core claim

The effects of radiation on a maximally entangled pair of fermions in a Bell state can be modeled as an open quantum system in which the Kraus operators that govern the system's evolution are identified with the integrated Altarelli-Parisi splitting functions.

What carries the argument

Identification of the Kraus operators for the open-system evolution of the Bell-state fermion pair with the integrated Altarelli-Parisi splitting functions.

If this is right

  • Different radiation processes (gluon emission, photon emission, etc.) produce quantitatively different reductions in the entanglement measure.
  • The model supplies a concrete, process-dependent correction factor that can be folded into existing spin-correlation analyses at colliders.
  • The same mapping supplies a way to predict the scale at which entanglement visibility drops below a detectable threshold as a function of radiated energy.

Where Pith is reading between the lines

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

  • The same identification may extend to other entangled particle pairs produced in high-energy collisions once appropriate splitting functions are substituted.
  • Including next-to-leading-order splitting or interference terms could reveal whether the leading-order Kraus map remains a good approximation or requires refinement.
  • Experimental programs could test the prediction by binning entanglement measures in events with varying amounts of additional radiation.

Load-bearing premise

The decoherence induced by radiation on the entangled fermion pair can be fully captured by identifying Kraus operators with integrated Altarelli-Parisi splitting functions without additional collider-specific kinematic corrections or higher-order interference terms.

What would settle it

A precision measurement of spin correlations in ttbar events at the LHC that compares the observed entanglement witness with and without the radiation-induced Kraus correction and finds a statistically significant mismatch.

Figures

Figures reproduced from arXiv: 2504.07030 by Alan J. Barr, Fabio Maltoni, Leonardo Satrioni, Rafael Aoude.

Figure 1
Figure 1. Figure 1: FIG. 1: Scalar boson decay to a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Concurrence for a scalar decay to [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Recent measurements at the Large Hadron Collider have observed entanglement in the spins of $t\bar t$ pairs. The effects of radiation, which are expected to lead to quantum decoherence and a reduction of entanglement, are generally neglected in such measurements. In this work we calculate the effects of decoherence from various different types of radiation for a maximally entangled pair of fermions -- a bipartite system of qubits in a Bell state. We identify the Kraus operators describing the evolution of the open quantum system with the integrated Altarelli-Parisi splitting functions.

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 paper claims to calculate the effects of radiation-induced decoherence on maximally entangled fermion pairs (a bipartite qubit system in a Bell state) at colliders such as the LHC, where ttbar spin entanglement has been measured. It proposes to identify the Kraus operators governing the open quantum system evolution directly with the integrated Altarelli-Parisi splitting functions for the relevant parton splittings.

Significance. If the proposed mapping holds after proper derivation, the result would supply a concrete, collider-physics-grounded channel for incorporating decoherence into entanglement observables, addressing an effect that is currently neglected in LHC analyses of top-quark spin correlations.

major comments (1)
  1. [Abstract] Abstract: the central claim equates the Kraus operators of the open-system channel to the integrated Altarelli-Parisi splitting functions P_{q→q}(z) and P_{q→g}(z) for a Bell state, yet supplies no derivation from the interaction Hamiltonian, no explicit partial trace over radiation degrees of freedom, and no demonstration that spin-dependent helicity amplitudes and joint phase-space measures leave no residual off-diagonal coherences after tracing. This identification is load-bearing for the entire result.
minor comments (1)
  1. [Abstract] The abstract refers to 'various different types of radiation' without enumerating which emissions (collinear, soft, non-collinear) are treated or how their contributions are combined.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and for recognizing the potential significance of incorporating radiation-induced decoherence into collider studies of top-quark spin entanglement. We address the major comment below and commit to revisions that will strengthen the presentation of the central mapping.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim equates the Kraus operators of the open-system channel to the integrated Altarelli-Parisi splitting functions P_{q→q}(z) and P_{q→g}(z) for a Bell state, yet supplies no derivation from the interaction Hamiltonian, no explicit partial trace over radiation degrees of freedom, and no demonstration that spin-dependent helicity amplitudes and joint phase-space measures leave no residual off-diagonal coherences after tracing. This identification is load-bearing for the entire result.

    Authors: We agree that the abstract states the identification concisely without reproducing the full technical steps. The manuscript motivates the mapping by noting that the integrated splitting functions encode the probability of emitting radiation carrying away momentum fraction z, which entangles the fermion spin with the unobserved radiation degrees of freedom; tracing over the latter then yields an effective channel on the spin qubits. To make this rigorous and address the referee’s valid concern, the revised manuscript will include a new dedicated section (or appendix) that begins from the relevant QED/QCD interaction Hamiltonian, computes the spin-dependent helicity amplitudes for the splitting processes, integrates over the radiation phase space with the appropriate joint measures, performs the partial trace explicitly, and demonstrates that residual off-diagonal coherences vanish for the symmetric integration employed. This will establish that the resulting operators are indeed the Kraus operators of a valid decoherence channel. revision: yes

Circularity Check

0 steps flagged

No circularity: central identification uses external standard results

full rationale

The paper's key step is an identification of Kraus operators for the open-system decoherence channel with integrated Altarelli-Parisi splitting functions, which are established QCD results external to this work. No equation or claim reduces by construction to a quantity fitted inside the paper, a self-definition, or a load-bearing self-citation chain. The derivation applies standard open-quantum-system formalism to a Bell state and imports the splitting functions as inputs rather than deriving them from the target entanglement observables, leaving the central claim independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The calculation relies on the standard framework of open quantum systems and the established Altarelli-Parisi splitting functions from QCD; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Radiation processes can be modeled as the environment causing decoherence in the open quantum system of the entangled fermion pair.
    This premise is required to apply the Kraus-operator formalism to the collider setting.

pith-pipeline@v0.9.0 · 5615 in / 1171 out tokens · 42874 ms · 2026-05-22T19:45:53.154754+00:00 · methodology

discussion (0)

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

Forward citations

Cited by 4 Pith papers

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

  1. Automated computation of spin-density matrices and quantum observables for collider physics

    hep-ph 2025-10 unverdicted novelty 7.0

    An automated framework in MadGraph5_aMC@NLO computes tree-level production spin-density matrices and quantum observables for generic collider processes, with validation on ttbar and VV and new applications to multi-to...

  2. Radiation effects on the entanglement of fermion pairs at colliders

    hep-ph 2026-04 unverdicted novelty 6.0

    Energetic radiation induces decoherence that significantly reduces entanglement in fermion pairs at colliders, with statistically significant signals observable in ttbar(g) at the LHC and tau pairs at Belle II.

  3. Spin Correlation and Quantum Entanglement of Fermion Pairs in Transversely Polarized $e^-e^+$ Collisions

    hep-ph 2026-04 unverdicted novelty 5.0

    Transverse polarization in e+e- collisions generates maximally entangled fermion pairs in QED processes and boosts entanglement in electroweak and Bhabha scattering.

  4. Understanding Bell locality tests at colliders

    hep-ph 2026-03 unverdicted novelty 4.0

    Under mild assumptions, local hidden variable theories become testable at colliders and can be disproved via Bell-like inequalities for muon and tau pairs.

Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages · cited by 4 Pith papers · 12 internal anchors

  1. [1]

    Parti- cle Theory at the Higgs Centre

    R.A. is supported by UK Research and In- novation (UKRI) under the UK government’s Hori- zon Europe Marie Sklodowska-Curie funding guarantee grant [EP/Z000947/1] and by the STFC grant “Parti- cle Theory at the Higgs Centre”. The work of AJB is funded in part through STFC grants ST/R002444/1 and ST/S000933/1. F.M. is partially supported by the PRIN2022 Gra...

    work page

  2. [2]

    Quantum entanglement

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009), arXiv:quant-ph/0702225

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  3. [3]

    Entanglement and quantum tomography with top quarks at the LHC,

    Y. Afik and J. R. M. n. de Nova, Eur. Phys. J. Plus 136, 907 (2021), arXiv:2003.02280 [quant-ph]

    work page arXiv 2021

  4. [4]

    Quantum tops at the LHC: from entanglement to Bell inequalities,

    C. Severi, C. D. E. Boschi, F. Maltoni, and M. Sioli, Eur. Phys. J. C 82, 285 (2022), arXiv:2110.10112 [hep-ph]

    work page arXiv 2022

  5. [5]

    Quantum SMEFT tomography: Top quark pair pro- duction at the LHC,

    R. Aoude, E. Madge, F. Maltoni, and L. Mantani, Phys. Rev. D 106, 055007 (2022), arXiv:2203.05619 [hep-ph]

    work page arXiv 2022

  6. [6]

    Afik and J.R.M.n

    Y. Afik and J. R. M. n. de Nova, Quantum 6, 820 (2022), arXiv:2203.05582 [quant-ph]

    work page arXiv 2022

  7. [7]

    Afik and J.R.M.n

    Y. Afik and J. R. M. n. de Nova, Phys. Rev. Lett. 130, 221801 (2023), arXiv:2209.03969 [quant-ph]

    work page arXiv 2023

  8. [8]

    A. J. Barr, P. Caban, and J. Rembieli´ nski, Quantum 7, 1070 (2023), arXiv:2204.11063 [quant-ph]

    work page arXiv 2023

  9. [9]

    Quantum entanglement and top spin correlations in SMEFT at higher orders,

    C. Severi and E. Vryonidou, JHEP 01, 148 (2023), arXiv:2210.09330 [hep-ph]

    work page arXiv 2023

  10. [10]

    Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of mas- sive particles,

    R. Ashby-Pickering, A. J. Barr, and A. Wierzchucka, JHEP 05, 020 (2023), arXiv:2209.13990 [quant-ph]

    work page arXiv 2023

  11. [11]

    Con- straining new physics in entangled two-qubit systems: top-quark, tau-lepton and photon pairs,

    M. Fabbrichesi, R. Floreanini, and E. Gabrielli, Eur. Phys. J. C 83, 162 (2023), arXiv:2208.11723 [hep-ph]

    work page arXiv 2023

  12. [12]

    Fabbri, J

    F. Fabbri, J. Howarth, and T. Maurin, Eur. Phys. J. C 84, 20 (2024), arXiv:2307.13783 [hep-ph]

    work page arXiv 2024

  13. [13]

    Aoude, E

    R. Aoude, E. Madge, F. Maltoni, and L. Mantani, JHEP 12, 017 (2023), arXiv:2307.09675 [hep-ph]

    work page arXiv 2023

  14. [14]

    T. Han, M. Low, and T. A. Wu, JHEP 07, 192 (2024), arXiv:2310.17696 [hep-ph]

    work page arXiv 2024

  15. [15]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Mar- zola, Eur. Phys. J. C 83, 823 (2023), arXiv:2302.00683 [hep-ph]

    work page arXiv 2023

  16. [16]

    Sakurai and M

    K. Sakurai and M. Spannowsky, Phys. Rev. Lett. 132, 151602 (2024), arXiv:2310.01477 [quant-ph]

    work page arXiv 2024

  17. [17]

    Altomonte and A.J

    C. Altomonte and A. J. Barr, Phys. Lett. B 847, 138303 (2023), arXiv:2312.02242 [hep-ph]. 6

    work page arXiv 2023

  18. [18]

    Y. Afik, Y. Kats, J. R. M. n. de Nova, A. Soffer, and D. Uzan, (2024), arXiv:2406.04402 [hep-ph]

    work page arXiv 2024

  19. [19]

    Grabarczyk, (2024), arXiv:2410.18022 [hep-ph]

    R. Grabarczyk, (2024), arXiv:2410.18022 [hep-ph]

    work page arXiv 2024

  20. [20]

    R. A. Morales, Eur. Phys. J. C 84, 581 (2024), arXiv:2403.18023 [hep-ph]

    work page arXiv 2024

  21. [21]

    C. D. White and M. J. White, Phys. Rev. D 110, 116016 (2024), arXiv:2406.07321 [hep-ph]

    work page arXiv 2024

  22. [22]

    Altomonte, A.J

    C. Altomonte, A. J. Barr, M. Eckstein, P. Horodecki, and K. Sakurai, (2024), arXiv:2412.01892 [hep-ph]

    work page arXiv 2024

  23. [23]

    T. Han, M. Low, N. McGinnis, and S. Su, (2024), arXiv:2412.21158 [hep-ph]

    work page arXiv 2024

  24. [24]

    Q. Liu, I. Low, and Z. Yin, (2025), arXiv:2503.03098 [quant-ph]

    work page arXiv 2025

  25. [25]

    A. J. Barr, M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Prog. Part. Nucl. Phys. 139, 104134 (2024), arXiv:2402.07972 [hep-ph]

    work page arXiv 2024

  26. [26]

    Observation of quantum entanglement in top-quark pairs using the ATLAS detector,

    G. Aad et al. (ATLAS), Nature 633, 542 (2024), arXiv:2311.07288 [hep-ex]

    work page arXiv 2024

  27. [27]

    Hayrapetyan et al

    A. Hayrapetyan et al. (CMS), Rept. Prog. Phys. 87, 117801 (2024), arXiv:2406.03976 [hep-ex]

    work page arXiv 2024

  28. [28]

    Hayrapetyan et al

    A. Hayrapetyan et al. (CMS), (2024), arXiv:2409.11067 [hep-ex]

    work page arXiv 2024

  29. [29]

    Behring, M

    A. Behring, M. Czakon, A. Mitov, A. S. Papanastasiou, and R. Poncelet, Phys. Rev. Lett. 123, 082001 (2019), arXiv:1901.05407 [hep-ph]

    work page arXiv 2019

  30. [30]

    Czakon, A

    M. Czakon, A. Mitov, and R. Poncelet, JHEP 05, 212 (2021), arXiv:2008.11133 [hep-ph]

    work page arXiv 2021

  31. [31]

    Mazzitelli, P

    J. Mazzitelli, P. F. Monni, P. Nason, E. Re, M. Wiese- mann, and G. Zanderighi, JHEP 04, 079 (2022), arXiv:2112.12135 [hep-ph]

    work page arXiv 2022

  32. [32]

    H. D. Zeh, Foundations of Physics 1, 69 (1970)

    work page 1970

  33. [33]

    W. H. Zurek, Phys. Rev. D 24, 1516 (1981)

    work page 1981

  34. [34]

    W. H. Zurek, Phys. Rev. D 26, 1862 (1982)

    work page 1982

  35. [35]

    Environment-induced deco- herence and the transition from quantum to classical,

    J. P. Paz and W. H. Zurek, “Environment-induced deco- herence and the transition from quantum to classical,” in Coherent atomic matter waves (Springer Berlin Heidel- berg) p. 533–614

    work page

  36. [36]

    Decoherence and the transition from quantum to classical – revisited,

    W. H. Zurek, “Decoherence and the transition from quantum to classical – revisited,” (2003), arXiv:quant- ph/0306072 [quant-ph]

    work page arXiv 2003

  37. [37]

    R. A. Bertlmann, Lect. Notes Phys. 689, 1 (2006), arXiv:quant-ph/0410028

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  38. [38]

    C. P. Burgess, T. Colas, R. Holman, and G. Kaplanek, JHEP 02, 204 (2025), arXiv:2411.09000 [hep-th]

    work page arXiv 2025

  39. [39]

    S. A. Salcedo, T. Colas, and E. Pajer, JHEP 10, 248 (2024), arXiv:2404.15416 [hep-th]

    work page arXiv 2024

  40. [40]

    S. A. Salcedo, T. Colas, and E. Pajer, JHEP 03, 138 (2025), arXiv:2412.12299 [hep-th]

    work page arXiv 2025

  41. [41]

    Infrared quantum information

    D. Carney, L. Chaurette, D. Neuenfeld, and G. W. Semenoff, Phys. Rev. Lett. 119, 180502 (2017), arXiv:1706.03782 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  42. [42]

    Dressed infrared quantum information

    D. Carney, L. Chaurette, D. Neuenfeld, and G. W. Semenoff, Phys. Rev. D 97, 025007 (2018), arXiv:1710.02531 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  43. [43]

    On the need for soft dressing

    D. Carney, L. Chaurette, D. Neuenfeld, and G. Semenoff, JHEP 09, 121 (2018), arXiv:1803.02370 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  44. [44]

    Neuenfeld, JHEP 11, 189 (2021), arXiv:1810.11477 [hep-th]

    D. Neuenfeld, JHEP 11, 189 (2021), arXiv:1810.11477 [hep-th]

    work page arXiv 2021

  45. [45]

    G. W. Semenoff, Springer Proc. Math. Stat. 335, 151 (2019), arXiv:1912.03187 [hep-th]

    work page arXiv 2019

  46. [46]

    Schlosshauer, Phys

    M. Schlosshauer, Phys. Rept. 831, 1 (2019), arXiv:1911.06282 [quant-ph]

    work page arXiv 2019

  47. [47]

    Aolita, F

    L. Aolita, F. de Melo, and L. Davidovich, Reports on Progress in Physics 78, 042001 (2015)

    work page 2015

  48. [48]

    J. C. Collins, Nuclear Physics B 304, 794 (1988)

    work page 1988

  49. [49]

    Knowles, Nuclear Physics B 304, 767 (1988)

    I. Knowles, Nuclear Physics B 304, 767 (1988)

    work page 1988

  50. [50]

    Parton showers with quantum interference

    Z. Nagy and D. E. Soper, JHEP 09, 114 (2007), arXiv:0706.0017 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  51. [51]

    Parton showers with quantum interference: leading color, with spin

    Z. Nagy and D. E. Soper, JHEP 07, 025 (2008), arXiv:0805.0216 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  52. [52]

    Parton showers with quantum interference: leading color, spin averaged

    Z. Nagy and D. E. Soper, JHEP 03, 030 (2008), arXiv:0801.1917 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  53. [53]

    Parton shower evolution with subleading color

    Z. Nagy and D. E. Soper, JHEP 06, 044 (2012), arXiv:1202.4496 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  54. [54]

    Richardson, JHEP 11, 029 (2001), arXiv:hep- ph/0110108

    P. Richardson, JHEP 11, 029 (2001), arXiv:hep- ph/0110108

    work page arXiv 2001

  55. [55]

    Spin Correlations in Parton Shower Simulations

    P. Richardson and S. Webster, Eur. Phys. J. C 80, 83 (2020), arXiv:1807.01955 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  56. [56]

    Hamilton, A

    K. Hamilton, A. Karlberg, G. P. Salam, L. Scyboz, and R. Verheyen, JHEP 03, 193 (2022), arXiv:2111.01161 [hep-ph]

    work page arXiv 2022

  57. [57]

    Kinoshita, Journal of Mathematical Physics 3, 650 (1962), https://pubs.aip.org/aip/jmp/article- pdf/3/4/650/19167464/650 1 online.pdf

    T. Kinoshita, Journal of Mathematical Physics 3, 650 (1962), https://pubs.aip.org/aip/jmp/article- pdf/3/4/650/19167464/650 1 online.pdf

    work page 1962

  58. [58]

    T. D. Lee and M. Nauenberg, Phys. Rev. 133, B1549 (1964)

    work page 1964

  59. [59]

    Braaten and J

    E. Braaten and J. P. Leveille, Phys. Rev. D 22, 715 (1980)

    work page 1980

  60. [60]

    Drees and K

    M. Drees and K. ichi Hikasa, Physics Letters B 240, 455 (1990)

    work page 1990

  61. [61]

    Janot, Phys

    P. Janot, Phys. Lett. B 223, 110 (1989)

    work page 1989

  62. [62]

    B. A. Kniehl, Nucl. Phys. B 376, 3 (1992)

    work page 1992

  63. [63]

    Altarelli and G

    G. Altarelli and G. Parisi, Nuclear Physics B 126, 298 (1977)

    work page 1977

  64. [64]

    Karlberg, G

    A. Karlberg, G. P. Salam, L. Scyboz, and R. Verheyen, Eur. Phys. J. C 81, 681 (2021), arXiv:2103.16526 [hep- ph]

    work page arXiv 2021

  65. [65]

    Kublbeck, H

    J. Kublbeck, H. Eck, and R. Mertig, Nucl. Phys. B Proc. Suppl. 29, 204 (1992)

    work page 1992

  66. [66]

    New Developments in FeynCalc 9.0

    V. Shtabovenko, R. Mertig, and F. Orellana, Comput. Phys. Commun. 207, 432 (2016), arXiv:1601.01167 [hep- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  67. [67]

    FeynCalc 9.3: New features and improvements

    V. Shtabovenko, R. Mertig, and F. Orellana, Comput. Phys. Commun. 256, 107478 (2020), arXiv:2001.04407 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  68. [68]

    Passarino and M

    G. Passarino and M. J. G. Veltman, Nucl. Phys. B 160, 151 (1979)

    work page 1979

  69. [69]

    Decoherence effects in entangled fermion pairs at colliders

    F. Maltoni, D. Pagani, and S. Tentori, JHEP 09, 098 (2024), arXiv:2406.06694 [hep-ph]. 1 Supplemental Material for “Decoherence effects in entangled fermion pairs at colliders” Rafael Aoude, Alan J. Barr, Fabio Maltoni and Leonardo Satrioni In this Supplemental Material, we provide details on the calculation of the main body as the explicit coefficients o...

    work page arXiv 2024