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Quantum correlations in deep-inelastic scattering can map the proton's internal transverse spin structure.

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2026-08-03 00:33 UTC pith:LPU7MTEI

load-bearing objection Clean proof-of-concept connecting DIS quantum correlation measures to transversity, with a real new extension to steering and discord—but the claimed direct mapping to tensor charges is a projection of the same fits, not an independent constraint. the 3 major comments →

arxiv 2607.28724 v1 pith:LPU7MTEI submitted 2026-07-30 hep-ph quant-ph

Hadron Structure from the Hierarchy of Quantum Correlations in Deep-Inelastic Scattering

Henry Bloss , TJ Hobbs , Navin McGinnis This is my paper
classification hep-ph quant-ph
keywords deep inelastic scatteringquantum entanglementquantum steeringquantum discordquantum magictransversity parton distribution functionstensor chargeshadron structure
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that the quantum correlations between the scattered electron and the struck quark in deep-inelastic scattering are a direct probe of the proton's transversity parton distribution functions, which encode the transverse spin of quarks inside a proton. Because these correlations are invariants of a reconstructed density matrix, measuring any one of them—entanglement, discord, steering, or magic—selects a band of allowed values for the proton's tensor charges δu and δd. The sharpest result is that the binary question of whether the final state is quark-steerable cleanly separates transversity fits that include lattice-QCD constraints from those that do not. This matters because the tensor charges are poorly determined and feed into searches for physics beyond the Standard Model, such as the neutron electric dipole moment.

Core claim

The paper establishes a calculable mapping from the quantum-information measures of the final-state electron–quark spin density matrix to the proton's tensor charges. At parton level, the struck quark inherits a fraction α(x,Q²) of the proton's transverse polarization, where α is the charge-weighted ratio of transversity to unpolarized PDFs. Quantum-information measures such as concurrence, quantum discord, steering, and magic are all functions of this α and the scattering angle, so different transversity fits produce distinct values of these measures at fixed kinematics. In particular, quark steerability acts as a threshold criterion: fits informed by lattice QCD predict steerable states at

What carries the argument

The central object is the Fano–Bloch decomposition of the two-qubit density matrix ρ_eq for the final-state electron and struck quark, whose coefficients are the measured single-spin polarizations and spin–spin correlation matrix. The argument is carried by the ratio α(x,Q²) = Σ_q e_q² h_{1,q}(x,Q²) / Σ_q e_q² f_q(x,Q²), which converts the proton's transverse polarization into the struck quark's transverse polarization, and by the steering inequality whose violation provides a binary steerability test that separates transversity scenarios.

Load-bearing premise

The calculation assumes the struck quark's transverse polarization is exactly the PDF ratio α times the proton's polarization, and that the quark's final-state spin is faithfully read out through its fragmentation into a jet; if hadronization or detector effects depolarize the quark, the measured quantum correlations no longer map to α, and the tensor-charge connection collapses.

What would settle it

Measure the spin-correlation matrix of the final-state electron and a jet in transversely polarized electron–proton scattering at a single kinematic point (e.g., x≈0.5, Q≈12 GeV). If the reconstructed density matrix shows a quark-steerable state for a transversity fit that predicts non-steerability (or vice versa), the mapping from quantum measures to tensor charges is falsified; alternatively, if the quark's reconstructed spin is systematically smaller than α b^p_⊥, the depolarization assumption fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • A measurement of any of the four quantum measures at a fixed DIS kinematic point maps to a definite band of allowed tensor charges (δu, δd), independent of the model assumptions of global fits.
  • Establishing quark steerability in the final state is a sharp, binary criterion that can distinguish transversity extractions made with lattice-QCD input from those made without.
  • The quantum measures constrain a flavor combination distinct from the isovector tensor charge g_T = δu − δd, offering a new handle for BSM searches such as the neutron electric dipole moment.
  • Quantum discord remains nonzero in regions where entanglement vanishes, so discord extends the probe to a wider range of scattering angles than concurrence alone.
  • The asymmetry between electron and quark discord and steering suggests the possibility of inferring the quark's quantum state from electron measurements alone, which is valuable since the quark is observed only through its jet.

Where Pith is reading between the lines

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

  • If the mapping survives realistic fragmentation and detector effects, the same technique could extend to other hard processes such as Drell-Yan, where a quark's transverse polarization enters the final-state density matrix, giving independent handles on transversity-like distributions.
  • The binary nature of steerability suggests a natural experimental test at a future electron-ion collider: simply establishing that the final state is steerable at one kinematic point would rule out all transversity fits that predict separable states, without needing precise values of the other measures.
  • Because α is flavor-charge-weighted, flavor-tagged final states (e.g., identifying charm or strangeness in the jet) would isolate individual quark flavors and could turn the quantum measures into flavor-by-flavor tensor-charge constraints.
  • The hierarchy among the measures—entanglement nested within steering, with discord extending beyond—could serve as a consistency check: if steering and concurrence disagree about the same state, that would signal unmodeled depolarization or higher-twist effects.

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

3 major / 5 minor

Summary. The paper proposes using quantum-information measures of the bipartite spin state of the final-state electron and struck quark in deep-inelastic scattering (DIS) as a probe of transversity PDFs and tensor charges. The authors derive the final-state density matrix rho_eq from leading-order partonic amplitudes (Supplemental Material), express it in Fano-Bloch form, and compute concurrence, stabilizer magic, quantum discord, and steering as functions of the initial transverse polarizations and the scattering angle. They parametrize the struck-quark transverse polarization by Eq. (15) as alpha(x,Q) times the proton polarization, where alpha is a charge-weighted ratio of transversity to unpolarized PDFs. Using five transversity fit ensembles (with and without lattice-QCD constraints), they show that at x=0.5, Q=12 GeV the quantum measures take different values for different fits, and they plot correlations between these measures and the tensor charges delta u, delta d defined by Eq. (17). The paper claims a direct, calculable mapping from the quantum invariants to tensor charges, with quark steerability as a binary discriminant between lattice-constrained and unconstrained fits, and discusses implications for BSM physics.

Significance. The parton-level derivation of rho_eq and the demonstration that multiple quantum-information measures have distinct sensitivity to transversity at a chosen DIS kinematic point are useful and timely contributions to the growing collider-QI literature. The paper goes beyond the previously studied back-scattering concurrence limit and shows that discord, magic, and steering have different angular and polarization dependence, which is a genuine addition. The use of five modern transversity fits, including lattice-constrained variants, makes the sensitivity study concrete and gives a sharp, in-principle falsifiable criterion: the presence or absence of quark steerability at a specified kinematic point. However, the central claim that these measures provide a direct mapping to the tensor charges is currently overstated: the mapping is mediated by the same PDF fits whose moments define the charges, and the experimental observability of the parton-level spin state is deferred. The paper's strengths are the analytic density-matrix formalism and the explicit fit comparison; its weakness is the gap between parton-level sensitivity and a demonstrated observable constraint on delta u, delta d.

major comments (3)
  1. [Constraints on Tensor Charges, Eq. (17) and Fig. 4] The central claim that a measurement of quantum correlations maps directly to delta u and delta d is not supported by the analysis as presented. The QI measures depend on the struck-quark polarization only through alpha(x,Q^2) at the single sampled point (x=0.5, Q=12 GeV; Eq. (15)), whereas delta u and delta d are x-integrals of the transversity PDFs (Eq. (17)). The bands in Fig. 4 are obtained by propagating the same five transversity fit ensembles through both alpha and the moment integral; they are therefore an internal projection of the fit ensembles, not an inference that proceeds 'entirely from invariants of the measured density matrix' as stated in the text. A state with the same measured invariants could correspond to different tensor charges if the true h_{1,q}(x) has an x-dependence not represented by the five fits. To make the 'direct mapping' claim defensible, the authors sho
  2. [Conclusions; Quantum State of DIS] The experimental program assumes that the spin state of the final-state struck quark can be reconstructed. The density matrix rho_eq in Eqs. (1)-(2) is defined for the electron and the parton-level quark, but the quark is not an asymptotic state; it is observed only through its fragmentation into a jet. The Conclusions state that the quark spin is 'accessed through its fragmentation into a jet' and that 'realistic fragmentation and detector effects' are left to future work. This is not a minor technicality: without a quantitative relation between the parton-level quark spin and the measured hadronic/jet observables (e.g., through spin-dependent fragmentation functions or jet polarimetry), the proposed quantum tomography of rho_eq cannot be performed. At present the paper demonstrates sensitivity at the parton level, not an observable prescription. The claims that steerability is a 'binar
  3. [Connection to Nonperturbative Models, Fig. 3 (lower left) and Fig. 4 (lower panels)] The binary steerability criterion is the sharpest advertised result, but its robustness is not quantified. The paper states that fits with lattice-QCD constraints are 'consistently quark-steerable at the 1 sigma level, unlike the latter,' but no number is given: what fraction of replicas in each of the five ensembles satisfies the steering inequality (Eq. (13)) at the reference point? How stable is this fraction under variation of x, Q, and sqrt(s) within the ranges shown in Fig. 1, or under higher-order QCD corrections to the hard-scattering matrix? Because the PDF ensembles carry probability distributions, a deterministic binary statement needs a statistical characterization. As written, the 'strong discriminator' could be a property of the specific fits at one kinematic point rather than a robust prediction. Please provide replication-level statistics or soften the claim accordingly.
minor comments (5)
  1. [Fig. 1] The caption does not define the white-dashed line in the middle panels. The text says it delineates the separable region as identified by the concurrence, but the caption should state this explicitly for the reader.
  2. [Eq. (11)] The steering inequality is presented without a citation to the original two-qubit steering criterion (e.g., Cavalcanti et al., Phys. Rev. Lett. 103, 170404 (2009)). A citation would help the uninitiated reader locate the derivation of Eq. (13).
  3. [Eq. (6)] The definition of the second stabilizer Renyi entropy for mixed states is not discussed; a brief remark on its validity for the mixed rho_eq considered here, or a reference, would be useful.
  4. [Quantum Hierarchy of DIS] The phrase 'the true classical-quantum boundary is measured through quantum discord' is imprecise; discord is one measure of non-classical correlations, not a unique boundary. Consider rewording to avoid overstatement.
  5. [Eq. (18)] The neutron EDM relation should specify the renormalization scale at which delta q^n and d_q are evaluated; this matters for the SMEFT interpretation of tensor charges.

Circularity Check

0 steps flagged

No significant circularity: QI measures are computed from the hard-scattering density matrix with standard PDF inputs; the tensor-charge correlation is a forward-model calibration, not a definitional identity. Only a minor, non-load-bearing self-citation.

full rationale

The derivation chain is: (1) the DIS final-state density matrix rho_eq is assembled from leading-order helicity amplitudes (Supplemental Eqs. S1-S5) with initial polarizations b_e^perp and b_q^perp; (2) the quantum measures (concurrence, magic, discord, steering) are functions of rho_eq; (3) the only nonperturbative input is b_q^perp = alpha b_p^perp, with alpha defined in Eq. (15) as a charge-weighted ratio of transversity to unpolarized PDFs; (4) tensor charges are defined as moments of h_{1,q} in Eq. (17). Steps (1)-(3) do not presuppose any tensor-charge value; the tensor charge does not enter rho_eq or any QI measure. The Fig. 4 correlation is produced by propagating independent external transversity fit ensembles (JAM, JAM3D, KPSY15) through both the QI observables and the moment integral. This is a forward-model calibration: for a given h_{1,q}, both quantities are computable, and the bands are posterior predictions of the fit ensemble. It is not an identity; a QI invariant at one (x,Q) determines alpha at that point, not the x-integral delta q; and it is not a fit of the QI invariant to delta q. The inference would become circular only if the same measured QI data had been used to build the transversity fits that define the bands, which is not done. The paper's claim that the inference proceeds entirely from invariants of the measured density matrix overstates the independence, because the inversion to delta q also uses the fit ensemble's functional forms and extrapolations; that is a correctness and interpretation concern, not a circular reduction. The only self-citation (Ref. [98], by two of the authors) appears in a general list of QI and DIS references and is not used to justify any load-bearing step. No step reduces to its own input by construction.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central result is a forward calculation from fitted PDFs to quantum measures; no new entities are introduced. The main hand-chosen inputs are the polarization settings and the single kinematic point, plus the QPM assumption that the quark spin follows the transversity ratio.

free parameters (4)
  • Initial electron transverse polarization b^e_⊥ = 0.7
    Fixed by hand in the text: "throughout, we fix the transverse polarization of the initial electron beam to b^e_⊥ = 0.7". All quantitative QI measures and the steering threshold depend on it; no experimental motivation or sensitivity scan given.
  • Initial proton transverse polarization b^p_⊥ = 0.7
    Fixed by hand; Fig. 3 caption fixes b^e_⊥ = b^p_⊥ = 0.7. The value is not justified by a specific EIC operating point.
  • Reference kinematics (x, Q, sqrt(s)) = x=0.5, Q=12 GeV, √s=20 GeV
    The discriminating-power claims (Figs. 3-4) are evaluated at this single point, where the spread in α(x) across fits is largest (Fig. 2). No x-scan or integrated sensitivity is shown; a different point could weaken the steering discriminant.
  • Quark polarization transfer α(x,Q²) (external PDF fits) = varies with x; see Fig. 2 for 1σ bands
    The mapping from quantum measures to tensor charges is mediated by the ratio of fitted transversity and unpolarized PDFs (Eqs. 14-15). The paper uses five existing fits as inputs; the "constraint" on δu,δd is therefore inherited from those fits.
axioms (5)
  • domain assumption Leading-order t-channel photon exchange dominates; amplitudes in Eq. (S1) are massless and leading-twist.
    Stated in Supplemental Material: "amplitudes are dominated by pure photon exchange and ... massless limit is applicable with only weak corrections." No NLO, Z/W, or higher-twist corrections are included.
  • domain assumption The struck quark's transverse polarization is b^q_⊥ = α b^p_⊥ with α given by Eq. (15).
    This QPM identification of transversity as quark transverse polarization is assumed, not derived; it is the bridge from the density matrix to PDFs.
  • domain assumption The final-state quark spin is accessible via jet fragmentation and dedicated polarimetry.
    Conclusions: "the quark spin accessed through its fragmentation into a jet and the electron spin through dedicated polarimetry." No fragmentation model or depolarization estimate is provided.
  • domain assumption Soffer bound suppresses heavier-quark transversity.
    Eq. (16) from Ref. [102] is used to justify keeping only u,d in the numerator of α.
  • domain assumption Light quarks are indistinguishable in the inclusive measurement; state treated as a charge-weighted flavor mixture.
    Stated after Eq. (15): "Because the light quarks are indistinguishable in the inclusive measurement, the spin state is treated as a flavor mixture."

pith-pipeline@v1.3.0-alltime-deepseek · 14279 in / 16230 out tokens · 149548 ms · 2026-08-03T00:33:19.689706+00:00 · methodology

0 comments
read the original abstract

We show that the hierarchy of quantum correlations produced in deep-inelastic scattering (DIS) can serve as a novel probe of the proton's nonperturbative structure. Specifically, we show that quantum entanglement, discord, steering, and magic provide nontrivial and complementary sensitivities to the nucleon's parton distribution functions (PDFs), particularly those encoding the transverse-spin polarization of the interacting quark. This connection leads to a unique probe of the proton's parton-level tensor charges with implications for beyond Standard Model (BSM) physics searches. We propose how quantum information measures can be utilized for precision studies of hadron structure at DIS experiments like the upcoming Electron-Ion Collider (EIC).

Figures

Figures reproduced from arXiv: 2607.28724 by Henry Bloss, Navin McGinnis, TJ Hobbs.

Figure 1
Figure 1. Figure 1: FIG. 1. The quantum concurrence (top left); magic (top [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. We plot [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The quantum concurrence, discord, steering, and [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The up- and down-quark tensor charges ( [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

105 extracted references · 78 linked inside Pith

  1. [1]

    J. D. Bjorken, Asymptotic Sum Rules at Infinite Mo- mentum, Phys. Rev.179, 1547 (1969)

    1969

  2. [2]

    Intersections of QIS and Theoretical Parti- cle Physics

    For DIS, the concurrence of thee −qfinal state is maximized in the back-scattering limit, cosθ=−1, where [69] C[ρeq] =b e ⊥bq ⊥ .(5) Thus, Bell states are produced whenb e ⊥ =b q ⊥ = 1. In addition to entanglement, quantum magic has be- come regarded as a crucial quantum resource for quan- tum computation. Quantum magic measures the failure of a quantum s...

  3. [3]

    Houet al., New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC, Phys

    T.-J. Houet al., New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC, Phys. Rev. D103, 014013 (2021), arXiv:1912.10053 [hep-ph]

    Pith/arXiv arXiv 2021

  4. [4]

    Moffat, W

    E. Moffat, W. Melnitchouk, T. C. Rogers, and N. Sato (Jefferson Lab Angular Momentum (JAM)), Simultane- ous Monte Carlo analysis of parton densities and frag- mentation functions, Phys. Rev. D104, 016015 (2021), arXiv:2101.04664 [hep-ph]

    Pith/arXiv arXiv 2021

  5. [5]

    Bailey, T

    S. Bailey, T. Cridge, L. A. Harland-Lang, A. D. Mar- tin, and R. S. Thorne, Parton distributions from LHC, HERA, Tevatron and fixed target data: MSHT20 PDFs, Eur. Phys. J. C81, 341 (2021), arXiv:2012.04684 [hep- ph]

    Pith/arXiv arXiv 2021

  6. [6]

    R. D. Ballet al.(NNPDF), The path to proton struc- ture at 1% accuracy, Eur. Phys. J. C82, 428 (2022), arXiv:2109.02653 [hep-ph]

    Pith/arXiv arXiv 2022

  7. [7]

    Z.-B. Kang, A. Prokudin, P. Sun, and F. Yuan, Ex- traction of Quark Transversity Distribution and Collins Fragmentation Functions with QCD Evolution, Phys. Rev. D93, 014009 (2016), arXiv:1505.05589 [hep-ph]

    Pith/arXiv arXiv 2016

  8. [8]

    Gamberg, M

    L. Gamberg, M. Malda, J. A. Miller, D. Pitonyak, A. Prokudin, and N. Sato (Jefferson Lab Angular Mo- mentum (JAM), Jefferson Lab Angular Momentum), Updated QCD global analysis of single transverse-spin asymmetries: Extracting H˜, and the role of the Sof- fer bound and lattice QCD, Phys. Rev. D106, 034014 (2022), arXiv:2205.00999 [hep-ph]

    Pith/arXiv arXiv 2022

  9. [9]

    Cocuzza, A

    C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl (Jefferson Lab Angular Momen- tum (JAM)), First simultaneous global QCD analysis of dihadron fragmentation functions and transversity par- ton distribution functions, Phys. Rev. D109, 034024 (2024), arXiv:2308.14857 [hep-ph]

    Pith/arXiv arXiv 2024

  10. [10]

    Chupp, P

    T. Chupp, P. Fierlinger, M. Ramsey-Musolf, and J. Singh, Electric dipole moments of atoms, molecules, nuclei, and particles, Rev. Mod. Phys.91, 015001 (2019), arXiv:1710.02504 [physics.atom-ph]

    Pith/arXiv arXiv 2019

  11. [11]

    Afik and J

    Y. Afik and J. R. M. de Nova, Entanglement and quan- tum tomography with top quarks at the LHC, Eur. Phys. J. Plus136, 907 (2021), arXiv:2003.02280 [quant- ph]

    Pith/arXiv arXiv 2021

  12. [12]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini, and G. Panizzo, Test- ing Bell Inequalities at the LHC with Top-Quark Pairs, Phys. Rev. Lett.127, 161801 (2021), arXiv:2102.11883 [hep-ph]

    Pith/arXiv arXiv 2021

  13. [13]

    Severi, C

    C. Severi, C. D. E. Boschi, F. Maltoni, and M. Sioli, Quantum tops at the LHC: from entanglement to Bell inequalities, Eur. Phys. J. C82, 285 (2022), arXiv:2110.10112 [hep-ph]

    Pith/arXiv arXiv 2022

  14. [14]

    Aoude, E

    R. Aoude, E. Madge, F. Maltoni, and L. Mantani, Quantum SMEFT tomography: Top quark pair pro- duction at the LHC, Phys. Rev. D106, 055007 (2022), arXiv:2203.05619 [hep-ph]

    Pith/arXiv arXiv 2022

  15. [15]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini, and E. Gabrielli, Con- straining new physics in entangled two-qubit systems: 7 top-quark, tau-lepton and photon pairs, Eur. Phys. J. C83, 162 (2023), arXiv:2208.11723 [hep-ph]

    Pith/arXiv arXiv 2023

  16. [16]

    Afik and J

    Y. Afik and J. R. M. de Nova, Quantum Discord and Steering in Top Quarks at the LHC, Phys. Rev. Lett. 130, 221801 (2023), arXiv:2209.03969 [quant-ph]

    Pith/arXiv arXiv 2023

  17. [17]

    Ashby-Pickering, A

    R. Ashby-Pickering, A. J. Barr, and A. Wierzchucka, Quantum state tomography, entanglement detection and Bell violation prospects in weak decays of mas- sive particles, JHEP05, 020, [Erratum: JHEP 03, 166 (2026)], arXiv:2209.13990 [quant-ph]

    arXiv 2026

  18. [18]

    Severi and E

    C. Severi and E. Vryonidou, Quantum entanglement and top spin correlations in SMEFT at higher orders, JHEP 01, 148, arXiv:2210.09330 [hep-ph]

    Pith/arXiv arXiv

  19. [19]

    M. M. Altakach, P. Lamba, F. Maltoni, K. Mawatari, and K. Sakurai, Quantum information and CP measure- ment in H→τ +τ − at future lepton colliders, Phys. Rev. D107, 093002 (2023), arXiv:2211.10513 [hep-ph]

    Pith/arXiv arXiv 2023

  20. [20]

    Z. Dong, D. Gon¸ calves, K. Kong, and A. Navarro, Entanglement and Bell inequalities with boosted tt¯, Phys. Rev. D109, 115023 (2024), arXiv:2305.07075 [hep-ph]

    Pith/arXiv arXiv 2024

  21. [21]

    R. A. Morales, Exploring Bell inequalities and quantum entanglement in vector boson scattering, Eur. Phys. J. Plus138, 1157 (2023), arXiv:2306.17247 [hep-ph]

    Pith/arXiv arXiv 2023

  22. [22]

    Aoude, E

    R. Aoude, E. Madge, F. Maltoni, and L. Mantani, Prob- ing new physics through entanglement in diboson pro- duction, JHEP12, 017, arXiv:2307.09675 [hep-ph]

    Pith/arXiv arXiv

  23. [23]

    Ma and T

    K. Ma and T. Li, Testing Bell inequality through h→τ τat CEPC*, Chin. Phys. C48, 103105 (2024), arXiv:2309.08103 [hep-ph]

    Pith/arXiv arXiv 2024

  24. [24]

    Sakurai and M

    K. Sakurai and M. Spannowsky, Three-Body Entangle- ment in Particle Decays, Phys. Rev. Lett.132, 151602 (2024), arXiv:2310.01477 [quant-ph]

    Pith/arXiv arXiv 2024

  25. [25]

    Bernal, Quantum tomography of helicity states for general scattering processes, Phys

    A. Bernal, Quantum tomography of helicity states for general scattering processes, Phys. Rev. D109, 116007 (2024), arXiv:2310.10838 [hep-ph]

    Pith/arXiv arXiv 2024

  26. [26]

    T. Han, M. Low, and T. A. Wu, Quantum entangle- ment and Bell inequality violation in semi-leptonic top decays, JHEP07, 192, arXiv:2310.17696 [hep-ph]

    Pith/arXiv arXiv

  27. [27]

    Altomonte and A

    C. Altomonte and A. J. Barr, Quantum state-channel duality for the calculation of Standard Model scat- tering amplitudes, Phys. Lett. B847, 138303 (2023), arXiv:2312.02242 [hep-ph]

    Pith/arXiv arXiv 2023

  28. [28]

    Ehat¨ aht, M

    K. Ehat¨ aht, M. Fabbrichesi, L. Marzola, and C. Veelken, Probing entanglement and testing Bell inequality viola- tion withe +e− →τ +τ − at Belle II, Phys. Rev. D109, 032005 (2024), arXiv:2311.17555 [hep-ph]

    Pith/arXiv arXiv 2024

  29. [29]

    Maltoni, C

    F. Maltoni, C. Severi, S. Tentori, and E. Vry- onidou, Quantum detection of new physics in top- quark pair production at the LHC, JHEP03, 099, arXiv:2401.08751 [hep-ph]

    Pith/arXiv arXiv

  30. [30]

    J. A. Aguilar-Saavedra, A closer look at post-decay t¯tentanglement, Phys. Rev. D109, 096027 (2024), arXiv:2401.10988 [hep-ph]

    Pith/arXiv arXiv 2024

  31. [31]

    Blasone, G

    M. Blasone, G. Lambiase, and B. Micciola, Entangle- ment distribution in Bhabha scattering with an en- tangled spectator particle, Phys. Rev. D109, 096022 (2024), arXiv:2401.10715 [quant-ph]

    Pith/arXiv arXiv 2024

  32. [32]

    A. J. Barr, M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Quantum entanglement and Bell in- equality violation at colliders, Prog. Part. Nucl. Phys. 139, 104134 (2024), arXiv:2402.07972 [hep-ph]

    Pith/arXiv arXiv 2024

  33. [33]

    Subba and R

    A. Subba and R. Rahaman, On bipartite and tripartite entanglement at present and future particle colliders, (2024), arXiv:2404.03292 [hep-ph]

    Pith/arXiv arXiv 2024

  34. [34]

    Bernal, P

    A. Bernal, P. Caban, and J. Rembieli´ nski, Entangle- ment and Bell inequality violation in vector diboson systems produced in decays of spin-0 particles, Sci. Rep. 15, 23410 (2025), arXiv:2405.16525 [hep-ph]

    Pith/arXiv arXiv 2025

  35. [35]

    Hayrapetyanet al.(CMS), Observation of quan- tum entanglement in top quark pair production in pro- ton–proton collisions at √s= 13 TeV, Rept

    A. Hayrapetyanet al.(CMS), Observation of quan- tum entanglement in top quark pair production in pro- ton–proton collisions at √s= 13 TeV, Rept. Prog. Phys. 87, 117801 (2024), arXiv:2406.03976 [hep-ex]

    Pith/arXiv arXiv 2024

  36. [36]

    S. Wu, C. Qian, Q. Wang, and X.-R. Zhou, Bell non- locality and entanglement in e+e-→YY¯at BESIII, Phys. Rev. D110, 054012 (2024), arXiv:2406.16298 [hep-ph]

    Pith/arXiv arXiv 2024

  37. [37]

    Demina and G

    R. Demina and G. Landi, Locality in collider tests of quantum mechanics with top quark pairs, Phys. Rev. D 111, 012013 (2025), arXiv:2407.15223 [hep-ph]

    Pith/arXiv arXiv 2025

  38. [38]

    Gabrielli and L

    E. Gabrielli and L. Marzola, Entanglement and Bell In- equality Violation inB→ϕϕDecays, Symmetry16, 1036 (2024), arXiv:2408.05010 [hep-ph]

    Pith/arXiv arXiv 2024

  39. [39]

    A. Ruzi, Y. Wu, R. Ding, S. Qian, A. M. Levin, and Q. Li, Testing Bell inequalities and probing quan- tum entanglement at a muon collider, JHEP10, 211, arXiv:2408.05429 [hep-ph]

    Pith/arXiv arXiv

  40. [40]

    A. Hayrapetyanet al.(CMS), Measurements of polar- ization and spin correlation and observation of entan- glement in top quark pairs using lepton+jets events from proton-proton collisions at s=13 TeV, Phys. Rev. D110, 112016 (2024), arXiv:2409.11067 [hep-ex]

    Pith/arXiv arXiv 2024

  41. [41]

    Du, X.-G

    Y. Du, X.-G. He, C.-W. Liu, and J.-P. Ma, Im- pact of parity violation on quantum entanglement and Bell nonlocality, Eur. Phys. J. C85, 1255 (2025), arXiv:2409.15418 [hep-ph]

    Pith/arXiv arXiv 2025

  42. [42]

    Ravina, Observation of quantum entanglement in top quark pairs at the ATLAS experiment, PoS LHCP2024, 327 (2025), arXiv:2410.04590 [hep-ex]

    B. Ravina, Observation of quantum entanglement in top quark pairs at the ATLAS experiment, PoS LHCP2024, 327 (2025), arXiv:2410.04590 [hep-ex]

    Pith/arXiv arXiv 2025

  43. [43]

    Cheng, T

    K. Cheng, T. Han, and M. Low, Quantum tomography at colliders: With or without decays, Phys. Lett. B868, 139675 (2025), arXiv:2410.08303 [hep-ph]

    Pith/arXiv arXiv 2025

  44. [44]

    Sullivan, Constraining New Physics withh→V V Tomography, (2024), arXiv:2410.10980 [hep-ph]

    M. Sullivan, Constraining New Physics withh→V V Tomography, (2024), arXiv:2410.10980 [hep-ph]

    Pith/arXiv arXiv 2024

  45. [45]

    Y. Wu, R. Jiang, A. Ruzi, Y. Ban, X. Yan, and Q. Li, Testing Bell inequalities and probing quantum entan- glement at CEPC, Phys. Rev. D111, 036008 (2025), arXiv:2410.17025 [hep-ph]

    Pith/arXiv arXiv 2025

  46. [46]

    A. Ruzi, L. Gao, Q. Li, C. Zhou, L. Chen, X. Zhang, Z. Sun, and Q. Li, Testing quantum entanglement via quantum state tomography with muons, J. Phys. G52, 075002 (2025), arXiv:2411.12518 [hep-ph]

    Pith/arXiv arXiv 2025

  47. [47]

    Altomonte, A

    C. Altomonte, A. J. Barr, M. Eckstein, P. Horodecki, and K. Sakurai, Prospects for quantum process to- mography at high energies, Quantum Sci. Technol.10, 045060 (2025), arXiv:2412.01892 [hep-ph]

    Pith/arXiv arXiv 2025

  48. [48]

    T. Han, M. Low, N. McGinnis, and S. Su, Measur- ing quantum discord at the LHC, JHEP05, 081, arXiv:2412.21158 [hep-ph]

    Pith/arXiv arXiv

  49. [49]

    Fabbrichesi, M

    M. Fabbrichesi, M. Low, and L. Marzola, Trace dis- tance between density matrices: A nifty tool in new- physics searches, Phys. Rev. D112, 013003 (2025), arXiv:2501.03311 [hep-ph]

    Pith/arXiv arXiv 2025

  50. [50]

    Cheng and B

    K. Cheng and B. Yan, Bell Inequality Violation of Light Quarks in Dihadron Pair Production at Lep- ton Colliders, Phys. Rev. Lett.135, 011902 (2025), arXiv:2501.03321 [hep-ph]. 8

    Pith/arXiv arXiv 2025

  51. [51]

    Lysak (Roman Lysak, ATLAS), Top quark spin and quantum entanglement in the ATLAS experiment, Sci- Post Phys

    R. Lysak (Roman Lysak, ATLAS), Top quark spin and quantum entanglement in the ATLAS experiment, Sci- Post Phys. Proc.18, 016 (2026), arXiv:2501.03755 [hep- ex]

    arXiv 2026

  52. [52]

    T. Han, M. Low, and Y. Su, Entanglement and Bell nonlocality inτ +τ − at the BEPC, JHEP10, 217, arXiv:2501.04801 [hep-ph]

    arXiv

  53. [53]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini, and L. Marzola, About Witnessing Bell Non-locality at Colliders, Found. Phys. 55, 83 (2025), arXiv:2503.18535 [quant-ph]

    arXiv 2025

  54. [54]

    Aoude, A

    R. Aoude, A. J. Barr, F. Maltoni, and L. Satrioni, De- coherence effects in entangled fermion pairs at collid- ers, Phys. Rev. D113, 076007 (2026), arXiv:2504.07030 [quant-ph]

    Pith/arXiv arXiv 2026

  55. [55]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini, and L. Marzola, Local vs. nonlocal entanglement in top-quark pairs at the LHC, JHEP11, 005, arXiv:2505.02902 [hep-ph]

    arXiv

  56. [56]

    Gon¸ calves, A

    D. Gon¸ calves, A. Kaladharan, F. Krauss, and A. Navarro, Quantum entanglement is quan- tum: ZZ production at the LHC, JHEP12, 122, arXiv:2505.12125 [hep-ph]

    arXiv

  57. [57]

    J. A. Aguilar-Saavedra, Quantum tomography beyond the leading order, Eur. Phys. J. C85, 969 (2025), arXiv:2505.11870 [hep-ph]

    Pith/arXiv arXiv 2025

  58. [58]

    Aoude, H

    R. Aoude, H. Banks, C. D. White, and M. J. White, Probing new physics in the top sector using quan- tum information, Phys. Rev. D113, 115066 (2026), arXiv:2505.12522 [hep-ph]

    Pith/arXiv arXiv 2026

  59. [59]

    Y. Afik, Y. Kats, J. R. M. de Nova, A. Soffer, and D. Uzan, Entanglement and Bell nonlocality with bottom-quark pairs at hadron colliders, Phys. Rev. D 111, L111902 (2025), arXiv:2406.04402 [hep-ph]

    Pith/arXiv arXiv 2025

  60. [60]

    W. Qi, Z. Guo, and B.-W. Xiao, Studying maxi- mal entanglement and Bell nonlocality at an electron- ion collider, Phys. Rev. D113, 054048 (2026), arXiv:2506.12889 [hep-ph]

    arXiv 2026

  61. [61]

    Gon¸ calves, A

    D. Gon¸ calves, A. Kaladharan, and A. Navarro, Higher- order corrections to quantum observables in h→WW ∗, JHEP11, 158, arXiv:2506.19951 [hep-ph]

    arXiv

  62. [62]

    Cheng, T

    K. Cheng, T. Han, M. Low, and T. A. Wu, Quantum Tomography in Neutral Meson and Antimeson Systems, Phys. Rev. Lett.136, 181803 (2026), arXiv:2507.12513 [hep-ph]

    Pith/arXiv arXiv 2026

  63. [63]

    Bechtle, C

    P. Bechtle, C. Breuning, H. K. Dreiner, and C. Duhr, A critical appraisal of tests of locality and of entan- glement versus non-entanglement at colliders, (2025), arXiv:2507.15947 [hep-ph]

    arXiv 2025

  64. [64]

    S. A. Abel, H. K. Dreiner, R. Sengupta, and L. Ubaldi, Colliders are Testing neither Locality via Bell’s In- equality nor Entanglement versus Non-Entanglement, (2025), arXiv:2507.15949 [hep-ph]

    Pith/arXiv arXiv 2025

  65. [65]

    S. Wu, C. Qian, Q. Wang, and Y.-G. Yang, Quan- tum steering and discord in hyperon-antihyperon sys- tem in electron-positron annihilation, Phys. Rev. D113, 056030 (2026), arXiv:2509.14990 [hep-ph]

    arXiv 2026

  66. [66]

    J. A. Aguilar-Saavedra, The top quark in 2025—In- ternational year of quantum science and technol- ogy, J. Subatomic Part. Cosmol.5, 100357 (2026), arXiv:2510.03212 [hep-ph]

    arXiv 2025

  67. [67]

    J. Pei, T. Li, L. Wu, X. Hao, and X. Wang, Bypassing spin-analyzing power dependence for quantum entan- glement at colliders: a case study of Λ Λ, JHEP07, 33, arXiv:2510.08031 [hep-ph]

    Pith/arXiv arXiv

  68. [68]

    Gu, S.-J

    J. Gu, S.-J. Lin, D. Y. Shao, L.-T. Wang, and S.-X. Yang, Decoherence in high energy collisions as renor- malization group flow, (2025), arXiv:2510.13951 [hep- ph]

    arXiv 2025

  69. [69]

    Yazgan, Measurements of top quark properties in CMS: tt¯tt¯spin density matrix, quantum entangle- ment and quantum magic, PoSEPS-HEP2025, 273 (2026), arXiv:2510.13743 [hep-ex]

    E. Yazgan, Measurements of top quark properties in CMS: tt¯tt¯spin density matrix, quantum entangle- ment and quantum magic, PoSEPS-HEP2025, 273 (2026), arXiv:2510.13743 [hep-ex]

    arXiv 2026

  70. [70]

    Cheng, T

    K. Cheng, T. Han, and S. Trifinopoulos, Quantum Information at the Electron-Ion Collider, (2025), arXiv:2510.23773 [hep-ph]

    arXiv 2025

  71. [71]

    Cao and F

    H. Cao and F. Petriello, Single-spin measurements and heavy new physics in the e+e-→tt¯process at an FCC- ee, Phys. Rev. D113, 035033 (2026), arXiv:2511.01994 [hep-ph]

    arXiv 2026

  72. [72]

    Hayrapetyanet al.(CMS), Characterization of the quantum state of top quark pairs produced in proton- proton collisions at s=13 TeV using the beam and helicity bases, Phys

    A. Hayrapetyanet al.(CMS), Characterization of the quantum state of top quark pairs produced in proton- proton collisions at s=13 TeV using the beam and helicity bases, Phys. Rev. D113, L051101 (2026), arXiv:2512.17557 [hep-ex]

    arXiv 2026

  73. [73]

    F. A. Jolly (ATLAS, CMS), Measurement of spin correlation and entanglement in ATLAS and CMS, J. Subatomic Part. Cosmol.5, 100358 (2026), arXiv:2601.04649 [hep-ex]

    Pith/arXiv arXiv 2026

  74. [74]

    C. D. Pardos (ATLAS, CMS), Entanglement effects at high energies (including top quark pair production at threshold) at ATLAS and CMS, PoSHQL2025, 004 (2026)

    2026

  75. [75]

    Y.-C. Guo, T. Han, M. Low, and Y. Su, Quan- tum Tomography of Fermion Pairs ine +e− Colli- sions: Longitudinal Beam Polarization Effects, (2026), arXiv:2602.02719 [hep-ph]

    arXiv 2026

  76. [76]

    Gabrielli and L

    E. Gabrielli and L. Marzola, Quantum entanglement and bell nonlocality at future lepton colliders, Eur. Phys. J. Plus141, 331 (2026), arXiv:2602.03960 [hep- ph]

    arXiv 2026

  77. [77]

    Zhang, X

    H.-W. Zhang, X. Cao, and T.-F. Feng, Manipulating Bell nonlocality and entanglement in polarized electron- positron annihilation, Phys. Rev. D113, 114022 (2026), arXiv:2602.10389 [hep-ph]

    Pith/arXiv arXiv 2026

  78. [78]

    B. Yang, Y. Zhang, Z. S. Wang, and X. Zhou, Entan- glement measures and Bell-type spin-correlation observ- ables in tau-lepton pairs at the Super Tau-Charm Fa- cility, (2026), arXiv:2603.05846 [hep-ph]

    arXiv 2026

  79. [79]

    J. A. Aguilar-Saavedra and P. P. Giardino, Quantum tomography ofH→ZZ, W Wbeyond leading order, (2026), arXiv:2603.11288 [hep-ph]

    arXiv 2026

  80. [80]

    Oussarhan, F

    Y. Oussarhan, F. Essaadi, S. Mouslih, M. Ouhammou, M. Jakha, S. Taj, and B. Manaut, Transfer of quantum coherence and entanglement in weake +e− →µ +µ− scattering through Z-boson exchange, Phys. Lett. B 876, 140408 (2026)

    2026

Showing first 80 references.