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This paper proposes an experimental strategy to test quantum entanglement in decays of the Higgs boson to pairs of W bosons at the Large Hadron Collider (LHC). Instead of using single-number expectation values of Bell-type operators (which can be distorted by detector effects and rare events), the authors build a continuous version of the Collins–Gisin–Linden–Massar–Popescu (CGLMP) inequality and perform hypothesis tests on the full distribution. To handle the main experimental difficulty — two invisible neutrinos in the final state of H → WW* → ℓν ℓν — they use conditional denoising diffusion probabilistic models (cDDPM). These machine-learning models produce an event-by-event, multidimensional unfolding of the measured data and can be applied directly to the full dataset, including backgrounds.
Concretely, the team compares the diffusion-based reconstruction to analytic reconstruction methods. They feed the reconstructed events into profile-likelihood hypothesis tests implemented with RooFit, a standard statistical tool in particle physics. Systematic uncertainties from background normalisation and from the shape of the unfolding are propagated through the fit. The continuous CGLMP observable is used as the fitted distribution, so the test distinguishes entangled states (the signal hypothesis) from separable states (the null hypothesis) by fitting the shape of that distribution rather than a single averaged number.
Why this matters: in the Standard Model the Higgs boson is expected to decay to a maximally entangled WW* spin state. Showing entanglement in this channel would extend tests of quantum mechanics to high-energy, relativistic particle processes and open a new way to probe the spin correlations in Higgs decays. The continuous-distribution approach reduces sensitivity to extreme events and detector outliers. The diffusion model for neutrino reconstruction is important because it can operate on measured events directly and does not require event-by-event truth labels at inference time, allowing the unfolding to be part of the analysis chain and to include background events naturally.
The authors report projected sensitivities from their simulation-based study. They find that the diffusion-based approach could reach about 3σ evidence for entanglement at roughly 555 inverse femtobarns (fb−1) of integrated luminosity, and exceed 5σ significance at about 1600 fb−1. These numbers are presented as projections and are compared to the expected reach of the High-Luminosity LHC (HL-LHC) programme.
Important caveats accompany these results. Reconstructing two invisible neutrinos is intrinsically difficult: experimental information constrains only the sum of transverse neutrino momenta, not each neutrino’s full momentum. Traditional analytic reconstructions use extra kinematic assumptions and fail for a significant fraction of events. The authors document limitations of alternative methods — for example, they report that classical unfolding of analytically reconstructed observables has zero coverage, and that OmniFold cannot handle a multi-background environment. The diffusion method appears promising in the simulated studies and the analysis includes propagated systematics, but the conclusions rely on simulations, detector modelling, and the robustness of the diffusion model training. Further experimental validation on real data would be needed before claiming an observation in the real LHC dataset.