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arXiv:2601.15748

Unveiling a Universal Formalism for Quantum Entanglement in Arbitrary Spin Decays

Junle Pei, Lina Wu, Dianwei Wang, X. Q. Hao, Tianjun Li

Published Jan 22, 2026• 0 citations
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Abstract

We present a comprehensive theoretical framework for probing quantum entanglement in the decay angular distributions of a spin-$S$ particle-antiparticle pair $A\bar{A}$, where each particle decays sequentially into a two-body final state, $A\to B+C$ and $\bar{A}\to\bar{B}+\bar{C}$, with $B(\bar{B})$ carrying spin $b$ and $C(\bar{C})$ being spinless. Starting from the most general polarized initial state, we derive the fully differential angular distribution $\mathcal{W}(θ_1,θ_2,ϕ_1,ϕ_2)$ and identify observables $\langle\cos(2S(ϕ_1\mpϕ_2))\rangle$ whose expectation values directly depend on the entanglement-sensitive coefficients $\text{Re}\left(α_{-S,\mp S}α_{S,\pm S}^*\right)$ of the initial state. The proportionality factor $\mathcal{C}(S,b)$ in these relations is computed explicitly. For bosonic decays ($b=0,1,2,\ldots$), $\mathcal{C}(S,b)$ is universal and independent of decay dynamics; in particular, $\mathcal{C}(S,0)=1/2$ for any $S$, and $\mathcal{C}(1,1)=1/8$, matching known results for $W^+W^-$ decays. For fermionic decays ($b=\frac{1}{2},\frac{3}{2},\frac{5}{2}\ldots$), $\mathcal{C}(S,b)$ depends explicitly on the spin analysis powers $α_{A/\bar{A}}$, making entanglement extraction more decay-dependent. We further demonstrate, within the context of $e^+e^-\toγ^*\to A\bar{A}$ production, how $α_{A/\bar{A}}$ can be determined experimentally using specific angular observables restricted to the beam-axis region. Our results highlight the special role of bosonic decays in providing clean, model-independent tests of quantum entanglement at colliders, while outlining a pathway for entanglement measurement in fermionic cases through supplementary polarization information.

DOI
10.48550/arxiv.2601.15748

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Entanglement is a key property of quantum systems. In this Letter the first measurements of quantum entanglement between spins in pairs of ZZZ bosons are reported, using proton-proton collision data from the Large Hadron Collider (LHC) at center-of-mass energies of 13 TeV and 13.6 TeV, recorded with the ATLAS detector. Measurements of angular observables sensitive to ZZ∗ZZ^*ZZ∗ spin-density-matrix elements in the H→ZZ∗→ℓ+ℓ−ℓ+ℓ−H\rightarrow ZZ^* \rightarrow \ell^+\ell^-\ell^+\ell^-H→ZZ∗→ℓ+ℓ−ℓ+ℓ− process yield coefficients C2,1,2,−1=−0.71±0.45C_{2,1,2,-1} = -0.71 \pm 0.45C2,1,2,−1​=−0.71±0.45 and C2,2,2,−2=0.08±0.44C_{2,2,2,-2}=0.08 \pm 0.44C2,2,2,−2​=0.08±0.44, consistent with their Standard Model predictions. A complementary hypothesis test using the full angular distribution, and relying on several Standard Model assumptions in the decays, provides substantially higher sensitivity to quantum correlations and disfavors the separable-state hypothesis at a significance of 4.7 standard deviations (expected 4.9σ4.9σ4.9σ) relative to the entangled Standard Model hypothesis. These results provide strong evidence of quantum entanglement between massive bosons (spin qutrits) at the electroweak scale.
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