pith. sign in

arxiv: 2606.24468 · v1 · pith:SBSLZDINnew · submitted 2026-06-23 · ✦ hep-ph · hep-ex· quant-ph

Entanglement and non-separability of momenta and coordinates at colliders

Marco Fabbrichesi , Roberto Floreanini , Luca Marzola This is my paper

Pith reviewed 2026-06-25 23:37 UTC · model grok-4.3

classification ✦ hep-ph hep-exquant-ph
keywords phase-space non-separabilityentanglementEPR correlationstau leptonscollider experimentsquantum mechanicsmomentum reconstruction
0
0 comments X

The pith

Phase-space non-separability of particle pairs can be tested at electron colliders using reconstructed tau lepton momenta.

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

The paper explores testing whether phase-space variables like momenta and coordinates are separable in collider experiments. It realizes an EPR-like setting with continuous variables rather than spins. By simulating tau lepton production and their decays, it shows through Monte Carlo that non-separability can be assessed experimentally. This extends entanglement studies to high-energy particle physics.

Core claim

The authors demonstrate that phase-space non-separability can be experimentally assessed in collider experiments by reconstructing the momenta of tau-lepton pairs from their decays into pions and neutrinos, and quantifying entanglement via hemispherical projections that map the continuous variables to a two-qubit system.

What carries the argument

Hemispherical projections reducing continuous momentum and coordinate variables to a two-qubit system to quantify entanglement in phase space.

If this is right

  • Non-separability of phase-space variables can be assessed using existing collider data on tau leptons.
  • EPR-like correlations in coordinates and momenta can be realized in actual particle production.
  • Entanglement in momenta of particle pairs can be quantified by reducing to qubit systems.
  • Tau lepton decays provide a practical channel for preserving phase-space correlations.

Where Pith is reading between the lines

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

  • If confirmed, this would allow tests of quantum mechanics foundations in high-energy regimes beyond spin measurements.
  • Similar methods might apply to other particle pairs produced at colliders for broader entanglement studies.
  • The approach could connect to questions about separability in quantum field theory.

Load-bearing premise

The reconstruction of tau-lepton momenta from their decays into pions and neutrinos preserves the necessary information about phase-space correlations without significant distortion from detector effects or neutrino reconstruction ambiguities.

What would settle it

A Monte Carlo simulation or actual data analysis showing that the reconstructed momenta yield no detectable EPR correlations or Bell inequality violations after accounting for all experimental effects would falsify the claim that non-separability can be assessed this way.

read the original abstract

We explore the possibility of testing in collider experiments whether phase-space variables are separable. We first study phase-space non-separability by means of EPR-like correlations. The original EPR setting is realized in an actual experiment, specifically in terms of coordinates and momenta, as per the original formulation, rather than spins or polarizations. We then show how to quantify the entanglement in the momenta of particle pairs by reducing the continuous variables to a two-qubit system through hemispherical projections. We discuss in detail the production of $\tau$-leptons at an electron collider, reconstructing the momenta of the former from their decays into pions and neutrinos, and demonstrate through a Monte Carlo simulation that phase-space non-separability can be experimentally assessed.

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 manuscript proposes testing whether phase-space variables (coordinates and momenta) are separable in collider experiments by realizing EPR-like correlations with tau-lepton pairs produced at an e+e- collider. Continuous variables are reduced to a two-qubit system via hemispherical projections, and the authors claim to demonstrate that phase-space non-separability is experimentally assessable through a Monte Carlo simulation of tau production and decays into pions and neutrinos.

Significance. If the Monte Carlo results hold under realistic conditions, the work would introduce a novel experimental probe of quantum correlations in phase space at colliders, extending EPR tests from discrete spins to continuous momentum-coordinate variables in high-energy physics.

major comments (1)
  1. [Monte Carlo simulation] Monte Carlo simulation section: The central claim that phase-space non-separability can be experimentally assessed rests on tau-lepton momentum reconstruction from pion+neutrino decays preserving EPR-like correlations after hemispherical projection. The manuscript must specify the neutrino four-momentum inference method (e.g., missing-energy constraints) and whether full detector response or smearing is included; without this, the simulated assessability may not survive realistic ambiguities.
minor comments (1)
  1. The abstract and introduction would benefit from an explicit statement of the collider energy and tau-pair production channel (e.g., via Z or photon) used in the simulation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: [Monte Carlo simulation] Monte Carlo simulation section: The central claim that phase-space non-separability can be experimentally assessed rests on tau-lepton momentum reconstruction from pion+neutrino decays preserving EPR-like correlations after hemispherical projection. The manuscript must specify the neutrino four-momentum inference method (e.g., missing-energy constraints) and whether full detector response or smearing is included; without this, the simulated assessability may not survive realistic ambiguities.

    Authors: We agree that the Monte Carlo section requires additional specification to support the central claim. In the revised manuscript we will add an explicit description of the neutrino four-momentum reconstruction: the neutrino momentum is inferred from missing transverse energy and momentum balance under the assumption that the visible pion and the neutrino are the only decay products of each tau. We will also state that the present simulation is performed at parton level without detector response or smearing, and we will include a brief discussion of this idealization as a limitation, noting that a full detector-level study would be needed to assess robustness under realistic conditions. revision: yes

Circularity Check

0 steps flagged

No circularity: Monte Carlo demonstration of assessability is an independent computational check

full rationale

The paper's chain consists of defining EPR-like correlations for continuous phase-space variables, reducing them to a two-qubit system via hemispherical projection, and then performing a Monte Carlo simulation of tau-pair production and decay at an e+e- collider to show that non-separability remains detectable after reconstruction. None of these steps reduces by construction to a fitted parameter, self-definition, or self-citation chain; the simulation functions as an external numerical test of the proposed reconstruction pipeline rather than a tautological restatement of the input assumptions. The central claim of experimental assessability therefore stands as self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No details available; abstract-only review prevents enumeration of free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5654 in / 986 out tokens · 20427 ms · 2026-06-25T23:37:01.679332+00:00 · methodology

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

31 extracted references · 9 linked inside Pith

  1. [1]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki,Quantum entanglement, Rev. Mod. Phys. 81(2009) 865–942, [quant-ph/0702225]

    Pith/arXiv arXiv 2009

  2. [2]

    Benatti, M

    F. Benatti, M. Fannes, R. Floreanini, and D. Petritis, Quantum Information, Computation and Cryptography. Springer Berlin, Heidelberg, 2010

    2010

  3. [3]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge University Press, 6, 2012

    2012

  4. [4]

    Bruss and G

    D. Bruss and G. Leuchs, Quantum Information: From Foundations to Quantum Technology Applications. Wiley, 2019

    2019

  5. [5]

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

    arXiv 2024

  6. [6]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola,Bell inequality is violated in B0 →J/ψ K ∗0(892)decays, Phys. Rev. D109(2024), no. 3 L031104, [arXiv:2305.04982]. [7]A TLASCollaboration, G. Aad et al.,Observation of quantum entanglement with top quarks at the ATLAS detector, Nature633(2024), no. 8030 542–547, [arXiv:2311.07288]. [8]CMSCollabora...

    arXiv 2024

  7. [7]

    Fabbrichesi, R

    M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola,Bell inequality is violated in charmonium decays, Phys. Rev. D110(2024), no. 5 053008, [arXiv:2406.17772]

    arXiv 2024

  8. [8]

    N. F. Mott,The wave mechanics ofα-ray track, Royal Society, Proc. A126 (800)(1929) 79

    1929

  9. [9]

    Figari and A

    R. Figari and A. Teta, Quantum dynamics of a particle in a tracking chamber. Springer Berlin, Heidelberg, 2014

    2014

  10. [10]

    W. H. Zurek,Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys.75 (May, 2003) 715–775

    2003

  11. [11]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen,Can quantum mechanical description of physical reality be considered complete?, Phys. Rev.47(1935) 777–780

    1935

  12. [12]

    Patil, S

    S. Patil, S. T¨ opfer, R. Swarnkar, S. Tovar-Perez, J. Moos, J. Fuenzalida, and M. Gr¨ afe,Advances in Position-Momentum Entanglement: A Versatile Tool for Quantum Technologies,arXiv:2505.22265

    arXiv

  13. [13]

    M. D. Reid,Demonstration of the einstein-podolsky-rosen paradox using nondegenerate parametric amplification, Phys. Rev. A40(Jul, 1989) 913–923

    1989

  14. [14]

    L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Inseparability Criterion for Continuous Variable Systems, Phys. Rev. Lett.84(2000), no. 12 2722, [quant-ph/9908056]

    Pith/arXiv arXiv 2000

  15. [15]

    M. D. Reid, P. D. Drummond, E. G. Cavalcanti, W. P. Bowen, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs,Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications, Rev. Mod. Phys.81(2009) 1727–1751, [arXiv:0806.0270]

    Pith/arXiv arXiv 2009

  16. [16]

    Giese,Entanglement and Its Verification: A Tutorial on Classical and Quantum Correlations, arXiv:2511.09507

    E. Giese,Entanglement and Its Verification: A Tutorial on Classical and Quantum Correlations, arXiv:2511.09507

    arXiv

  17. [17]

    Mancini, V

    S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Entangling macroscopic oscillators exploiting radiation pressure, Phys. Rev. Lett.88(2002) 120401, [quant-ph/0108044]

    Pith/arXiv arXiv 2002

  18. [18]

    Alwall, P

    J. Alwall, P. Demin, S. de Visscher, R. Frederix, M. Herquet, F. Maltoni, T. Plehn, D. L. Rainwater, and T. Stelzer,MadGraph/MadEvent v4: The New Web Generation, JHEP09(2007) 028, [arXiv:0706.2334]

    Pith/arXiv arXiv 2007

  19. [19]

    Hagiwara, T

    K. Hagiwara, T. Li, K. Mawatari, and J. Nakamura, TauDecay: a library to simulate polarized tau decays via FeynRules and MadGraph5, Eur. Phys. J. C73(2013) 2489, [arXiv:1212.6247]. [22]Belle-IICollaboration, W. Altmannshofer et al.,The Belle II Physics Book, PTEP2019(2019), no. 12 123C01, [arXiv:1808.10567]. [Erratum: PTEP 2020, 029201 (2020)]

    Pith/arXiv arXiv 2013

  20. [20]

    S. Seki, I. Y. Park, and S.-J. Sin,Variation of Entanglement Entropy in Scattering Process, Phys. Lett. B743(2015) 147–153, [arXiv:1412.7894]

    Pith/arXiv arXiv 2015

  21. [21]

    Peschanski and S

    R. Peschanski and S. Seki,Entanglement Entropy of Scattering Particles, Phys. Lett. B758(2016) 89–92, [arXiv:1602.00720]

    Pith/arXiv arXiv 2016

  22. [22]

    Peschanski and S

    R. Peschanski and S. Seki,Evaluation of Entanglement Entropy in High Energy Elastic Scattering, Phys. Rev. D100(2019), no. 7 076012, [arXiv:1906.09696]

    arXiv 2019

  23. [23]

    Faleiro, H

    R. Faleiro, H. A. S. Costa, R. Pav˜ ao, B. Hiller, A. H. Blin, and M. Sampaio,Perturbative approach to entanglement generation in QFT using the S matrix, J. Phys. A53(2020), no. 36 365301, [arXiv:1607.01715]

    arXiv 2020

  24. [24]

    Kowalska and E

    K. Kowalska and E. M. Sessolo,Entanglement in flavored scalar scattering, JHEP07(2024) 156, [arXiv:2404.13743]

    arXiv 2024

  25. [25]

    Low and Z

    I. Low and Z. Yin,Elastic cross section is entanglement entropy, Phys. Rev. D111(2025), no. 6 065027, [arXiv:2410.22414]

    arXiv 2025

  26. [26]

    C. M. Sou, Y. Wang, and X. Zhang,Entanglement features in scattering mediated by heavy particles, JHEP 10(2025) 003, [arXiv:2507.03555]

    arXiv 2025

  27. [27]

    Peschanski and S

    R. Peschanski and S. Seki,Entanglement in Elastic and Inelastic Two-particle Scatterings at High Energy, arXiv:2601.22502

    Pith/arXiv arXiv

  28. [28]

    J. S. Bell and A. Aspect, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press, 2 ed., 2004

    2004

  29. [29]

    A. M. Cetto, L. De la Pe˜ na, and E. Santos,A Bell inequality involving position, momentum and energy, Phys. Lett. A113(1985) 304–306

    1985

  30. [30]

    J. A. Aguilar-Saavedra,Momentum entanglement at colliders: theH→W W, ZZcase,arXiv:2512.02104

    arXiv

  31. [31]

    L. R. Kasday,Proc. Intern. School of Physics Enrico Fermi, 1971, p. 195,

    1971