arxiv: 2604.27130 · v1 · submitted 2026-04-29 · ✦ hep-ph · hep-ex· quant-ph

Recognition: unknown

Optimised Inference of Quantum Phenomena in High-Energy Collider Experiments

Hai-Chau Nguyen , Gilberto Tetlalmatzi-Xolocotzi , Carmen Diez Pardos , Otfried G\"uhne , Matthias Kleinmann

Authors on Pith no claims yet

Pith reviewed 2026-05-07 08:31 UTC · model grok-4.3

classification ✦ hep-ph hep-exquant-ph

keywords shadow tomographyspin entanglementcollider physicsquantum informationtop quarksrelativistic effectshigh-energy physicsspin correlations

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The pith

Shadow tomography framework characterizes spin-spin correlations in collider experiments despite uncontrolled momenta.

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

The paper introduces a general framework using shadow tomography to characterize spin-spin correlations among particles produced in high-energy collisions. In these experiments relativistic motion couples each particle's spin to its momentum, and experimenters have no control over the outgoing momenta, so conventional entanglement tests that require momentum knowledge cannot be applied directly. Shadow tomography reconstructs the necessary correlation operators from a limited set of measurements performed on the final-state particles. The authors demonstrate the method on top-quark pair production at the LHC as a concrete case. Because the same approach works for arbitrary final states, it supplies a practical route for extracting quantum-information quantities from existing and future collider datasets.

Core claim

We develop a general framework based on shadow tomography techniques for characterising spin-spin correlations in collider experiments. This improves the analysis of spin-spin entanglement, where relativistic motion couples spin and momentum and the momenta of the investigated particles are not under experimental control. As a proof of concept we illustrate the application of our formalism to top quark pair production at the Large Hadron Collider at CERN. The framework, however, is general and flexible and can be readily applied to more complex final states and systems with more particles.

What carries the argument

Shadow tomography protocol adapted to relativistic spin-momentum coupling with uncontrolled momenta, reconstructing spin-correlation operators directly from collider measurement data.

If this is right

Quantitative entanglement measures become extractable from top-quark pair data collected at the LHC.
The same reconstruction applies without modification to any other two- or multi-particle final state produced in collisions.
No additional detector hardware or beam-line modifications are required to obtain the correlations.
Existing archived collider datasets can be re-analysed for spin correlations using only post-processing.

Where Pith is reading between the lines

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

The technique could be combined with machine-learning classifiers to further reduce the number of events needed for a given precision.
Analogous adaptations might allow quantum-information analyses of relativistic particles in astrophysical or cosmological settings where momenta are likewise uncontrolled.
If the framework remains accurate at higher energies, collider data could serve as a testbed for quantum foundations under conditions unreachable in low-energy laboratories.

Load-bearing premise

Shadow tomography can be applied directly to relativistic systems with spin-momentum coupling and no momentum control without introducing large systematic errors in the extracted correlations.

What would settle it

Apply the framework to Monte Carlo simulations of top-quark pairs whose true spin correlations are known from exact matrix-element calculations; the reconstructed values must agree with the known values within statistical uncertainty.

Figures

Figures reproduced from arXiv: 2604.27130 by Carmen Diez Pardos, Gilberto Tetlalmatzi-Xolocotzi, Hai-Chau Nguyen, Matthias Kleinmann, Otfried G\"uhne.

**Figure 1.** Figure 1: Average values of partial-transpose based witness view at source ↗

**Figure 2.** Figure 2: Correlation matrix of the tt¯ spin obtained using 107 Monte Carlo simulated events. The uncertainties quoted correspond to the statistical uncertainty, which is known to underestimate the uncertainty in experiments. Every entry, except for the upper left 4×4 matrix, is predicted to be zero. The correlations are computed as the mean value of 4πY Re l,m(ˆut)Y Re l ′ ,m′ (ˆut¯), where Y Re denotes the real s… view at source ↗

**Figure 3.** Figure 3: Regions where the entanglement witnesses view at source ↗

**Figure 4.** Figure 4: Histogram of the top quark momentum in the view at source ↗

read the original abstract

Entanglement, a fundamental phenomenon of quantum theory, has recently been observed in processes in high-energy physics. This opens new avenues for probing quantum effects in relativistic regimes, but also poses conceptual and technical challenges. We develop a general framework based on shadow tomography techniques for characterising spin-spin correlations in collider experiments. This improves the analysis of spin-spin entanglement, where relativistic motion couples spin and momentum and the momenta of the investigated particles are not under experimental control. As a proof of concept we illustrate the application of our formalism to top quark pair production at the Large Hadron Collider at CERN. The framework, however, is general and flexible and can be readily applied to more complex final states and systems with more particles.

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.

Desk Editor's Note private letter to a colleague

The paper adapts shadow tomography to spin correlations in collider data with uncontrolled momenta, but the adaptation to fixed decay projectors risks bias that the abstract does not resolve.

read the letter

The core claim is a general framework that ports shadow tomography to collider settings so experimenters can estimate spin-spin entanglement even when particle momenta are not controlled and relativity mixes spin with momentum. They give a proof-of-concept for top-quark pairs at the LHC and say the method extends to other final states. That extension is the genuinely new piece; prior work on collider entanglement has not used classical shadows in this uncontrolled-momentum regime. The write-up is clear about the motivation and keeps the formalism flexible, which is useful for people who want to try the approach on different processes. The citation pattern looks standard and does not hide circularity. The main soft spot is exactly the one the stress-test flags. Spin information in these experiments arrives only through angular distributions of decay products, which define a small, momentum-dependent set of effective projectors. If the paper does not show that the resulting POVM still permits unbiased shadow estimation after averaging over the event sample, or that positivity of the reconstructed two-spin state is preserved, then the entanglement witnesses could be systematically off. The abstract gives no derivations or error budgets, so it is impossible to judge whether that step holds. A reader working at the quantum-information/high-energy-physics boundary would get a practical tool to test, provided the technical details survive scrutiny. The paper is coherent on its own terms and shows honest engagement with the literature, so it is worth a referee’s time even if revisions are needed on the measurement model.

Referee Report

1 major / 2 minor

Summary. The manuscript develops a general framework based on shadow tomography techniques for characterising spin-spin correlations in collider experiments. It addresses challenges from relativistic spin-momentum coupling and uncontrolled particle momenta, with a proof-of-concept application to top-quark pair production at the LHC. The framework is presented as flexible and applicable to more complex final states.

Significance. If the adaptation of shadow tomography to decay-based measurements in the relativistic regime proves unbiased and positivity-preserving, the work would offer a systematic method for quantum tomography in high-energy physics. This could enable more reliable entanglement witnesses for spin correlations at colliders, extending quantum information tools to regimes with fixed projectors and boost-induced effects.

major comments (1)

§3 (Application to top-pair production): The central claim requires that the effective POVM defined by angular distributions of W bosons and b-jets, combined with lab-frame boosts, permits unbiased classical-shadow estimation of the two-spin density matrix. The manuscript does not provide an explicit calculation showing that momentum averaging over the event sample eliminates systematic bias or rank deficiency in the estimator; without this, the reconstructed entanglement witnesses may be invalid.

minor comments (2)

§2 (Framework): The notation for the random unitary ensemble and the classical-shadow estimator could be made more explicit to clarify how it differs from standard shadow tomography in the presence of momentum-dependent projectors.
The abstract and introduction would benefit from a brief statement of the key assumption regarding the completeness of the decay-based projectors.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting this important technical point regarding the unbiasedness of the shadow estimator in the top-pair application. We address the comment below.

read point-by-point responses

Referee: §3 (Application to top-pair production): The central claim requires that the effective POVM defined by angular distributions of W bosons and b-jets, combined with lab-frame boosts, permits unbiased classical-shadow estimation of the two-spin density matrix. The manuscript does not provide an explicit calculation showing that momentum averaging over the event sample eliminates systematic bias or rank deficiency in the estimator; without this, the reconstructed entanglement witnesses may be invalid.

Authors: We agree that an explicit verification strengthens the central claim. The general shadow-tomography construction in Section 2 is formulated so that the estimator remains unbiased under averaging provided the effective POVM is informationally complete on average; the linearity of the reconstruction map ensures that integration over the boost distribution (which is independent of the spin state) does not introduce systematic bias. Nevertheless, we acknowledge that the manuscript does not display the explicit matrix-level calculation for the top-pair kinematics. In the revised version we will add an appendix that (i) writes the averaged shadow map explicitly, (ii) verifies that the resulting estimator is trace-preserving and unbiased for any two-qubit state, and (iii) confirms that the sampled angular distributions yield a full-rank frame operator, thereby eliminating rank deficiency. This addition will be placed immediately after the description of the top-pair analysis in Section 3. revision: yes

Circularity Check

0 steps flagged

No circularity: framework adapts established shadow tomography to collider spin correlations as an independent extension

full rationale

The derivation chain begins from established shadow tomography (random unitaries plus computational-basis measurements) and applies it to the new setting of relativistic spin-momentum coupling with uncontrolled momenta in collider events. The top-quark pair production example functions as a proof-of-concept illustration rather than a fitted or self-referential result. No equation or step reduces by construction to its own inputs, no parameter is fitted on a subset and then relabeled a prediction, and no load-bearing uniqueness theorem or ansatz is imported solely via self-citation. The central claim therefore remains self-contained against external benchmarks in quantum information and high-energy physics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that shadow tomography remains effective when applied to relativistic spin-momentum entangled states with experimentally uncontrollable momenta; no free parameters or new entities are mentioned in the abstract.

axioms (1)

domain assumption Shadow tomography techniques can be adapted to characterise spin-spin correlations in relativistic particle systems at colliders.
Invoked as the basis for the general framework in the abstract.

pith-pipeline@v0.9.0 · 5437 in / 1218 out tokens · 60449 ms · 2026-05-07T08:31:33.686242+00:00 · methodology

discussion (0)

Reference graph

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We boost all momenta and the beam axis to the centre of mass system with velocityβ cms = (pt +p ¯t)/(p0 t +p 0¯t ), yieldingp ′ t,p ′¯t,p ′ a,p ′ b, andb ′

T ransformation to the helicity reference frame In the Monte Carlo data, for each event the 4-momentumpt (p¯t) of the top (antitop) quark and the 4-momentap a,p b of the corresponding decay leptons are given in the lab frame with the beam axisb= (1,0,0,1)inz-direction. We boost all momenta and the beam axis to the centre of mass system with velocityβ cms ...
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,−1, Y Re l,0 =Y l,0, Y Re l,m = √ 2(−1)m Re(Yl,m)form= 1,

Computing the correlation matrix To avoid complex numbers in the correlation matrix we use the real spherical harmonics Y Re l,m = √ 2(−1)m Im(Yl,−m)form=−l, . . . ,−1, Y Re l,0 =Y l,0, Y Re l,m = √ 2(−1)m Re(Yl,m)form= 1, . . . , l, (C2) which also from an orthonormal function system. In terms ofx= cosφsinϑ,y= sinφsinϑ,z= cosϑ, the lowest order real sphe...
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Here we briefly point out that classical shadows allow us to efficiently compute the variance directly

Computing the variance in shadow tomography In the analysis in the main text we use the statistical uncertainty, computed as the sample standard deviation. Here we briefly point out that classical shadows allow us to efficiently compute the variance directly. For this we assume that the dataˆ uis produced by measuring the POVMF(ˆ u)and that we evaluate a ...
[47]

Data consistency test To illustrate how the correlation matrix in Fig. 2 of the main text is able to detect physical inconsistencies, we generated 10 millionp→t ¯tevents in MadGraph5_aMC@NLO [43] at NLO accuracy in QCD, inducing decays into electrons and muons throughMadSpin. This sample satisfies two consistency tests: (i) the mean value of the shadow op...
[48]

In general, a density operatorϱof two spin-1 2 particles is entangled if and only if its partial transposeΛ[ϱ]has a negative eigenvalue [23, 24]

Entanglement Witnesses To detect entanglement for all top quark momenta, we construct a momentum-dependent witness. In general, a density operatorϱof two spin-1 2 particles is entangled if and only if its partial transposeΛ[ϱ]has a negative eigenvalue [23, 24]. Here, the partial transpose is the transpose of either of the spins in a fixed basis; we useΛ[|...