Pith. sign in

REVIEW 3 major objections 4 minor 36 references

This paper argues that Bell-type inequalities can be formulated in particle flavor space using Standard Model interactions, and that their operator algebra predicts a violation of Bell's bound for an entangled down-strange quark state.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Mass-identification, kaon-decay, and weak-mixing observables can be cast as spin-like operators whose correlations violate a Bell-type bound (0.44+0.90=1.34>1) in an idealized Gedanken framework.

T0 review reviewed 2026-08-03 challenge →

load-bearing objection Correct and candid spin-Bell rephrasing in flavor space; the abstract overstates 'exclusion' beyond what the stated assumptions allow. the 3 major comments →

arxiv 2512.23855 v2 pith:7V2S45KT submitted 2025-12-29 hep-ph hep-exhep-thquant-ph

Gedanken Experiments of Entanglement in Particle Physics: Interactions, Operators and Bell Inequalities in Flavor Space

Corbin Pacheco (Wayne State University) , Nausheen R. Shah (Wayne State University) This is my paper
classification hep-ph hep-exhep-thquant-ph
keywords Bell inequalitiesflavor entanglementStandard Model operatorsCabibbo angleneutral kaonschiralityquantum information at collidersoperator-level diagnostics
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 reading

This paper tries to establish that the Standard Model's own flavor interactions—detector mass identification, charged-current weak mixing, and kaon-mediated flavor change—are sufficient to define a Bell-type test, without any external or tunable spin analyzers. On the maximally entangled state |χ⟩=(|dd̄⟩+|ss̄⟩)/√2, the resulting operators produce correlation functions E(a,b)=0, E(a,c)=sin2θ_c, and E(b,c)=cos2θ_c, which plugged into Bell's inequality |E(a,b)-E(a,c)| ≤ 1−E(b,c) reduce to |sin2θ_c|+cos2θ_c ≤ 1. Using the measured Cabibbo angle 2θ_c ≈ 26°, the left-hand side evaluates to about 1.34, violating the bound, and the paper attributes this to the non-commutative operator structure rather than to kinematic correlations or new physics. If accepted, this shows that collider event-counting in flavor channels can certify non-classical correlations at the operator level, and it gives experimental correlation patterns that any local hidden-variable description of flavor must fail to reproduce.

Core claim

The paper's central claim is that three Standard Model interaction-defined flavor operators emulate the spin operators needed for Bell's inequality: F_ID = σ_z (mass identification in the detector), F_W = U†F_IDU = cos2θ_c σ_z + sin2θ_c σ_x (charged-current weak mixing), and F_F = F_K†F_D F_K (flavor flip via neutral-kaon creation and decay). Acting on the entangled flavor state |χ⟩=(|dd̄⟩+|ss̄⟩)/√2, these produce the correlators E(a,b)=0, E(a,c)=sin2θ_c, and E(b,c)=cos2θ_c, so Bell's inequality |E(a,b)-E(a,c)| ≤ 1−E(b,c) reduces to |sin2θ_c|+cos2θ_c ≤ 1, which the empirical Cabibbo angle 2θ_c ≈ 26° violates (≈1.34 > 1). The point is that the violation follows purely from the operator algebr

What carries the argument

The central object is the triple of dichotomic flavor operators on the two-generation subspace {|m1⟩,|m2⟩}: mass identification F_ID = σ_z; charged-current weak mixing F_W = U†F_IDU = cos2θ_c σ_z + sin2θ_c σ_x, where θ_c is the Cabibbo angle; and flavor flip F_F = F_K†F_D F_K, built from the kaon creation operator F_K (d→K0, s→K̄0) and the flavor decay operator F_D whose eigenstates are K_S (+1, 2π decay) and K_L (−1, 3π decay). This triple is the exact analog of the spin settings S_z, S_x, S_θ required for Bell's inequality, and its non-commutativity is what allows the quantum correlators to exceed the local hidden-variable bound.

Load-bearing premise

The load-bearing premise is that the three interaction contexts probe identically prepared copies of the same two-particle state with settings that function as free choices; the paper explicitly concedes it does not enforce strict measurement independence in the Bell sense, and the flavor-flip setting is implemented through a non-unitary kaon creation operator, so the measured subsystem is not identical across runs.

What would settle it

Measure the three correlators on identically prepared |χ⟩=(|dd̄⟩+|ss̄⟩)/√2 events with an experimental setup that can tag d/d̄, s/s̄, K_S/K_L, and up/charm final states and can assign interaction context before the outcomes are known. If |E(a,b)-E(a,c)| + E(b,c) ≤ 1 is observed within uncertainties, the predicted algebraic violation is absent. Alternatively, recompute the correlators using a full quantum measurement description of hadronization instead of the idealized F_K and check whether the Bell bound |sin2θ_c|+cos2θ_c ≤ 1 is still crossed.

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

If this is right

  • Bell-type consistency conditions apply to flavor observables: for the entangled state |χ⟩, a local hidden-variable description would have to satisfy |E(a,b)-E(a,c)| + E(b,c) ≤ 1, while the SM operators predict 1.34, so such a description is excluded under the stated assumptions.
  • The violation is algebraic, so it is inherited by any process that prepares the same flavor-entangled state; realistic production and hadronization reduce fidelity but do not change the operator structure.
  • The same three-operator construction transfers to the first- and second-generation lepton sector by replacing quark flavor labels, although neutrino detection and absence of bound states make experimental access harder.
  • The predicted joint-event pattern—E(a,b)=0, E(a,c)=sin2θ_c, E(b,c)=cos2θ_c—is a concrete counting signature that can be compared with collider data once the three interaction contexts are identified in events.

Where Pith is reading between the lines

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

  • Editorial inference: because the paper's own assumptions exclude strict measurement independence, the realistic experimental reading is a contextuality test rather than a loophole-free spacelike Bell test; fixing the free-choice gap by designing an event trigger uncorrelated with hidden variables would be the decisive step toward a stricter collider Bell test.
  • Editorial inference: the flavor-flip run changes the measured subsystem from a bare quark to a neutral kaon, so the three correlators are not measurements of literally the same observable on the same system; replacing the idealized F_K with a genuine quantum measurement description of hadronization is a direct way to check whether the violation survives.
  • Editorial inference: the same operator-algebraic template (identification, flip, rotated mixing) could be applied to other two-level physical systems where three interaction-defined dichotomic observables exist, such as neutrino flavor with matter-induced mixing, giving a wider class of Bell-type inequalities from natural Hamiltonians rather than detector design.
  • Editorial inference: if the correlation pattern is measured, the exact numerical value via sin2θ_c and cos2θ_c is a parameter-free prediction; deviations would quantify both experimental infidelity and the breakdown of the quark-to-kaon map, separating the two failure modes.
Share X Bluesky LinkedIn Reddit HN

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 / 4 minor

Summary. The paper constructs flavor-space binary operators—mass identification (F_ID), flavor flip (F_F), and charged-current weak mixing (F_W)—in analogy with the Pauli spin operators, and applies them to the maximally entangled down-strange quark state |χ⟩=(|dd̄⟩+|ss̄⟩)/√2. The central derivation yields the correlators E(a,b)=0, E(a,c)=sin 2θ_c, E(b,c)=cos 2θ_c (Eqs. 51–53), and then evaluates the Bell-type inequality |E(a,b)−E(a,c)| ≤ 1−E(b,c) (Eq. 55) to obtain |sin 2θ_c|+cos 2θ_c ≤ 1, which is violated numerically as ≈1.34 (Eq. 57). The paper interprets this as excluding non-contextual local descriptions under stated assumptions, and discusses how the correlations might be probed in collider data.

Significance. If the central claim were fully supported, the paper would provide a genuinely new operator-level diagnostic of quantum incompatibility in flavor space, using only Standard Model interactions and the measured Cabibbo angle. The algebraic verification is transparent and correct: the three correlators follow from the operator definitions, and the Bell-inequality evaluation is arithmetically sound. The authors also deserve credit for explicitly acknowledging limitations of the Gedanken setup, including the non-unitarity of hadronization and the lack of strict measurement independence. However, as the paper itself states these limitations, the advertised conclusion that the violation 'excludes non-contextual local descriptions' is not actually derivable from the presented assumptions. The value of the work lies in its explicit operator-level formulation and its honest framing as a Gedanken experiment, not in a loophole-free exclusion of local realism.

major comments (3)
  1. [Sec. IV A, Eq. (55)] The Bell-type bound in Eq. (55) is derived from Eq. (6), which assumes a setting-independent hidden-variable distribution ρ(λ). The manuscript explicitly states in Sec. IV A that 'this framework does not enforce strict measurement independence in the Bell sense' because the effective measurement context is inferred from observed event signatures. Without measurement independence, Eq. (55) does not constrain general LHV models: a setting-dependent ρ_{xy}(λ) can reproduce the observed correlators exactly. Thus the abstract's 'excluding non-contextual local descriptions' is not supported by the formal argument. The authors should either add settings independence as an explicit idealization and explain its physical meaning, or weaken the conclusion to a statement about the operator algebra under that additional assumption.
  2. [Sec. III B, Eqs. (36)–(42) and footnote 2] The 'flavor flip' operator F_F is built from the kaon creation operator F_K, which footnote 2 admits is 'not a physical unitary operator' and is at best an effective POVM element. Consequently, in runs that use F_F (i.e., the (a,b) and (a,c) settings) Alice's subsystem is a neutral kaon, a composite hadron, while in the (b,c) run it is a bare quark. The three correlators are therefore not evaluated on identically prepared copies of the same bipartite state |χ⟩; the measurement 'settings' change the identity of one subsystem. This undermines the premise, stated in Sec. IV A, that all correlators 'originate from the same underlying quantum state prepared at production.' The authors should justify treating the kaon as a faithful proxy for the quark flavor qubit, or explicitly restrict the claim to an operator-algebraic consistency condition that does not require the same physical state acro
  3. [Abstract and Sec. V] The paper's central claim is phrased as 'violate Bell-type bounds, excluding non-contextual local descriptions under the stated assumptions.' But the stated assumptions include the absence of strict measurement independence and the use of a non-unitary hadronization operator. Under those assumptions, the Bell-type inequality does not exclude any LHV model; it only demonstrates that a particular set of SM-inspired operator correlators violates an inequality that would be valid in an idealized Bell test with free settings. The conclusion in Sec. V that violations 'certify the necessity of entanglement and contextuality in the flavor sector' is too strong. The authors should rephrase the claims to emphasize that the violation is a property of the operator algebra, conditional on additional idealizations that are not currently specified or experimentally realized.
minor comments (4)
  1. [Eq. (54), text below] In the paragraph following Eq. (54), the text says 'Hence, E(b,c) = ⟨F^A_F ⊗ F^B_W⟩_χ = ...' but the expression shown corresponds to E(a,c), not E(b,c). The label should be corrected.
  2. [Abstract and Sec. I] The phrase 'non-contextual local descriptions' mixes two distinct concepts. Bell inequalities test local hidden variables under measurement independence; non-contextuality is a separate assumption. The manuscript should use consistent terminology (e.g., 'local hidden-variable models') or define precisely what 'non-contextual local' means in this operator-level context.
  3. [Eq. (35)] The identification F_W ≡ F(2θ_c) means the 'predicted' violation is fixed by the choice of rotation angle equal to the Cabibbo angle. This is not a free-parameter prediction but a construction. The text should clarify that the violation holds for any θ_c ∈ (0, π/4), so the nonzero Cabibbo angle is sufficient, but the numerical value 1.34 is input-dependent.
  4. [Table II] In the (a,b) row, the probabilities for the four joint outcomes are listed as 1/4 each. This is correct only if the kaon decay and the mass measurement are independent given the state, which is true by construction, but the table could state this explicitly to avoid confusion.

Circularity Check

0 steps flagged

No significant circularity: the flavor correlators are derived from SM operator definitions and compared against an independent Bell bound; the paper's admitted loopholes are validity limitations, not circular reductions.

full rationale

No load-bearing circular step can be exhibited. The derivation chain is: define F_ID=σ_z (Eq. 26); define the flavor-flip operator via kaon operators (Eqs. 36–42); define F_W=U^† F_ID U with U the Cabibbo rotation (Eqs. 32–35); evaluate E(a,b), E(a,c), E(b,c) on |χ⟩ (Eqs. 51–53); then compare with the independent Bell bound of Eq. (6)/(55). The correlators follow algebraically from the operator definitions and the external measured Cabibbo angle; they are not fitted to the Bell inequality, and the Bell bound is an external benchmark. No uniqueness theorem or author-loaded ansatz is imported, and there are no self-citations. The paper is candid in Sec. IV A that 'this framework does not enforce strict measurement independence in the Bell sense,' and footnote 2 notes F_K is 'not a physical unitary operator.' These statements weaken the strength of the abstract's exclusion claim, but they describe loopholes or idealization gaps, not a circular derivation: if measurement independence were restored, the calculation would be a genuine prediction from the SM operator algebra. The central inequality violation is therefore not equivalent to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 2 invented entities

No fitted or hand-chosen numerical parameters: the only numeric input is the PDG Cabibbo angle θ_c≈13°, an external benchmark used in Eq. (57). The load-bearing structure is carried by axioms: the (standard) LHV Bell bound; the closed two-generation qubit assumption; the non-physical kaon-bridge operator F_K (author-disclosed); the waived measurement-independence premise (Sec. IV A); and the idealized coherent input state. Two invented entities supply the physical content: F_K (the 'graviton' of this construction — it exists only to make the third setting exist) and the coherent state |χ⟩, whose coherence is the entire source of the violation (a flavor-diagonal mixture gives E=0 for the (a,b) and (a,c) correlators and no violation).

axioms (5)
  • standard math Bell's inequality Eq. (6) correctly bounds local hidden-variable correlations for binary ±1 outcomes with perfect same-setting correlation (E(b,b)=+1).
    The LHV derivation is standard (Bell 1964 / CH-style); used in Sec. II and applied in Eqs. (55)–(57). Verified correct for the correlated state |χ⟩.
  • domain assumption The two-generation flavor space {|m1⟩,|m2⟩} is a closed qubit with the SU(2) algebra of Eq. (30) and a single well-defined mixing angle θ_c.
    The real SM has three generations, particle/antiparticle and up/down distinctions that the paper deliberately collapses (footnote 1), and open hadronization; the closed-qubit assumption is what makes the spin-operator correspondence exact.
  • ad hoc to paper Kaon creation/decay implements a valid binary measurement F_F via F_K (Eq. 36) and F_D (Eq. 39).
    Footnote 2 concedes F_K is 'not a physical unitary operator' and hadronization is an open quantum process mapped to an 'effective binary POVM'; footnote 4 concedes F_K† acts on the bra, not a dynamical inversion. The third Bell setting rests entirely on this idealized bridge.
  • domain assumption The correlators come from identically prepared copies of |χ⟩ with settings uncorrelated to hidden variables (measurement independence).
    Sec. IV A states the framework 'does not enforce strict measurement independence in the Bell sense'; without free choice, LHV models with settings correlated to λ reproduce any correlation, so Eq. (6) cannot exclude LHV. This is the load-bearing premise of the 'excluding non-contextual local descriptions' claim.
  • ad hoc to paper The idealized entangled state |χ⟩=(|dd̄⟩+|ss̄⟩)/√2 is available and coherent.
    Sec. IV A: 'We treat |χ⟩ as an idealized input state of the Gedanken experiment.' No SM process (e.g., Z decay) produces a coherent superposition of flavor eigenstates; a flavor-diagonal mixture gives E(a,c)=E(a,b)=0 and no violation.
invented entities (2)
  • Kaon creation operator F_K (Eq. 36) no independent evidence
    purpose: Bridges quark flavor states (|d⟩,|s⟩) to neutral-kaon states (|K⁰⟩,|K̄⁰⟩) so that the kaon decay operator F_D defines the flavor-flip setting F_F ≡ F_K† F_D F_K (Eq. 42).
    The paper itself states (footnote 2) that F_K 'should be understood as an idealized element of the Gedanken experiment... rather than a physical unitary operator' and (footnote 4) that F_K† is not a dynamical inversion. It is a non-dynamical map, the analogue of the 'graviton problem': it supplies the missing third measurement setting without any experimental handle.
  • Coherent entangled flavor state |χ⟩=(|dd̄⟩+|ss̄⟩)/√2 no independent evidence
    purpose: Input two-particle state for the Bell-type correlators in Sec. IV; its flavor-space coherence is what makes E(a,c)=sin2θ_c nonzero.
    Admitted as idealized (Sec. IV A). If the actual production density matrix is diagonal in flavor (as in Z decays), the correlators E(a,b) and E(a,c) vanish and the inequality is satisfied — so the violation depends entirely on this postulated coherence.

reviewed 2026-08-03 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Gedanken Experiments of Entanglement in Particle Physics: Interactions, Operators and Bell Inequalities in Flavor Space." pith.science (2026). https://pith.science/paper/7V2S45KT

@misc{pith2026251223855,
  author       = {Pith},
  title        = {Pith review of: Gedanken Experiments of Entanglement in Particle Physics: Interactions, Operators and Bell Inequalities in Flavor Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7V2S45KT}},
  note         = {Machine review of arXiv:2512.23855}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

In this article we explore ideas from quantum entanglement which can be meaningfully formulated and tested in the collider environment. We propose Bell-type inequalities as operator-level diagnostics of quantum incompatibility in particle-physics systems. We construct flavor operators associated with mass identification, flavor change, and charged-current weak mixing which arise from fundamental interactions in the Standard Model. We treat these interactions as alternative measurement settings in a Gendanken experiment. For entangled two-particle states, these operators generate nontrivial correlations that violate Bell-type bounds, excluding non-contextual local descriptions under the stated assumptions. These violations arise from the algebraic structure of the operators rather than from kinematic correlations or exotic dynamics. We discuss how the predicted correlation patterns may be probed with experimental data, clarifying the scope and limitations of Bell-type reasoning in particle physics.

discussion (0)

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

Reference graph

Works this paper leans on

36 extracted references · 13 linked inside Pith

  1. [1]

    Siwach, A

    P. Siwach, A. B. Balantekin, A. V. Patwardhan, and A. M. Suliga, Exploring entanglement and spec- tral split correlations in three-flavor collective neu- trino oscillations, Physical Review D111, 10.1103/phys- revd.111.063038 (2025)

    doi:10.1103/phys- 2025

  2. [2]

    Q. Liu, I. Low, and Z. Yin, A Quantum Computational Determination of the Weak Mixing Angle in the Standard Model, (2025), arXiv:2509.18251 [hep-ph]

    arXiv 2025

  3. [3]

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

    Pith/arXiv arXiv 2025

  4. [4]

    Thaler and S

    J. Thaler and S. Trifinopoulos, Flavor patterns of fun- damental particles from quantum entanglement?, Phys. Rev. D111, 056021 (2025), arXiv:2410.23343 [hep-ph]

    Pith/arXiv arXiv 2025

  5. [5]

    T.-R. Hu, S. Chen, K. Sone, F.-K. Guo, T. Hyodo, and I. Low, Entanglement suppression and emergent symme- tries in hadron scatterings, in21st International Con- ference on Hadron Spectroscopy and Structure(2025) arXiv:2507.22694 [hep-ph]

    arXiv 2025

  6. [6]

    Carena, G

    M. Carena, G. Coloretti, W. Liu, M. Littmann, I. Low, and C. E. M. Wagner, Entanglement maximization and mirror symmetry in two-Higgs-doublet models, JHEP08, 016, arXiv:2505.00873 [hep-ph]

    Pith/arXiv arXiv

  7. [7]

    Busoni, J

    G. Busoni, J. Gargalionis, E. N. V. Wallace, and M. J. White, Emergent symmetry in a two-Higgs-doublet model from quantum information and nonstabilizerness, Phys. Rev. D112, 035022 (2025), arXiv:2506.01314 [hep- ph]

    Pith/arXiv arXiv 2025

  8. [8]

    Fedida and A

    S. Fedida and A. Serafini, Tree-level entanglement in quantum electrodynamics, Physical Review D107, 10.1103/physrevd.107.116007 (2023)

    doi:10.1103/physrevd.107.116007 2023

  9. [9]

    Carena, I

    M. Carena, I. Low, C. E. M. Wagner, and M.-L. Xiao, Entanglement suppression, enhanced symmetry and a standard-model-like higgs boson, Phys. Rev. D109, L051901 (2024), arXiv:2307.08112 [hep-ph]

    Pith/arXiv arXiv 2024

  10. [10]

    S. R. Beane and R. C. Farrell, Geometry and entangle- ment in the scattering matrix, Annals of Physics433, 168581 (2021)

    2021

  11. [11]

    S. R. Beane, D. B. Kaplan, N. Klco, and M. J. Savage, Entanglement suppression and emergent symmetries of strong interactions, Phys. Rev. Lett.122, 102001 (2019)

    2019

  12. [12]

    Cervera-Lierta, J

    A. Cervera-Lierta, J. Latorre, J. Rojo, and L. Rottoli, Maximal entanglement in high energy physics, SciPost Physics3, 10.21468/scipostphys.3.5.036 (2017)

    doi:10.21468/scipostphys.3.5.036 2017

  13. [13]

    Q. Liu, I. Low, and T. Mehen, Minimal entanglement and emergent symmetries in low-energy QCD, Phys. Rev. C 107, 025204 (2023), arXiv:2210.12085 [quant-ph]

    Pith/arXiv arXiv 2023

  14. [14]

    J. S. Bell, On the einstein podolsky rosen paradox, Physics Physique Fizika1, 195 (1964)

    1964

  15. [15]

    ATLAS Collaboration, Measurements of spin correlation in top–antitop quark events at √s= 13 tev using the atlas detector, JHEP05, 176, arXiv:2302.10093 [hep-ex]

    Pith/arXiv arXiv

  16. [16]

    Study of spin correlations in Higgs boson decays to four leptons at CMS, (2025)

    2025

  17. [17]

    Y. Afik, A. E. C´ arcamo Hern´ andez, M. Dalchenko, I. Ginzburg, M. Khabibullin, V. Shtabovenko,et al., En- tanglement and bell nonlocality with bottom-quark pairs at hadron colliders, (2024), arXiv:2406.04402 [hep-ph]

    Pith/arXiv arXiv 2024

  18. [18]

    Low, Addressing local realism through Bell tests at colliders, Phys

    M. Low, Addressing local realism through Bell tests at colliders, Phys. Rev. D112, 096008 (2025), arXiv:2508.10979 [hep-ph]

    arXiv 2025

  19. [19]

    CMS Collaboration, Observation of quantum entangle- ment in top quark pair production in proton-proton colli- sions at √s= 13 tev, (2024), arXiv:2406.03976 [hep-ex]

    Pith/arXiv arXiv 2024

  20. [20]

    T. Han, M. Low, and Y. Su, Entanglement and bell non- locality inτ +τ − at the bepc, (2025), arXiv:2501.04801 [hep-ph]

    arXiv 2025

  21. [21]

    Hanet al., Quantum entanglement and bell inequality violation at the lhc, (2023), arXiv:2310.17696 [hep-ph]

    T. Hanet al., Quantum entanglement and bell inequality violation at the lhc, (2023), arXiv:2310.17696 [hep-ph]

    Pith/arXiv arXiv 2023

  22. [22]

    J. F. Clauser and A. Shimony, Bell’s theorem. experimen- tal tests and implications, Reports on Progress in Physics 41, 1881 (1978)

    1978

  23. [23]

    Abramsky and L

    S. Abramsky and L. Hardy, Logical Bell Inequalities, Phys. Rev. A85, 062114 (2012), arXiv:1203.1352 [quant- ph]

    Pith/arXiv arXiv 2012

  24. [24]

    S. A. Abel, H. K. Dreiner, R. Sengupta, and L. Ubaldi, Colliders are testing neither locality via bell’s inequal- ity nor entanglement versus non-entanglement, JHEP06, 258, arXiv:2507.15949 [hep-ph]

    Pith/arXiv arXiv

  25. [25]

    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

  26. [26]

    S. Li, W. Shen, and J. M. Yang, Can Bell inequalities be tested via scattering cross-section at colliders ?, Eur. Phys. J. C84, 1195 (2024), arXiv:2401.01162 [hep-th]

    Pith/arXiv arXiv 2024

  27. [27]

    S. Abel, M. Dittmar, and H. Dreiner, Testing locality at colliders via bell’s inequality?, Physics Letters B280, 304 (1992)

    1992

  28. [28]

    Abramsky and A

    S. Abramsky and A. Brandenburger, The sheaf-theoretic structure of non-locality and contextuality, New J. Phys. 13, 113036 (2011)

    2011

  29. [29]

    Brunner, D

    N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell nonlocality, Rev. Mod. Phys.86, 419 (2014)

    2014

  30. [30]

    Fine, Hidden variables, joint probability, and the bell inequalities, Phys

    A. Fine, Hidden variables, joint probability, and the bell inequalities, Phys. Rev. Lett.48, 291 (1982)

    1982

  31. [31]

    P. D. Group, Review of particle physics, Phys. Rev. D 110, 030001 (2024)

    2024

  32. [32]

    Fabre and N

    C. Fabre and N. Treps, Modes and states in quantum optics, Rev. Mod. Phys.92, 035005 (2020)

    2020

  33. [33]

    Romero and G

    J. Romero and G. Milburn, Photonic quantum comput- ing (2025), arXiv:2404.03367 [quant-ph]

    arXiv 2025

  34. [34]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information, 10th ed. (Cambridge Univer- sity Press, 2010)

    2010

  35. [35]

    B. C. Hiesmayr and A. Di Domenico, Neutral kaons as an open quantum system, Eur. Phys. J. C72, 2036 (2012)

    2036

  36. [36]

    J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Evidence for the 2πdecay of thek 0 2 meson, Phys. Rev. Lett.13, 138 (1964)

    1964

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.