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Measurements of $Z$-boson pair entanglement in decays of Higgs bosons at the ATLAS experiment

G. Aad, Erlend Aakvaag, B. Abbott, Sara Abdelhameed, K. Abeling, Nils Julius Abicht, S. H. Abidi, Mohammed Aboelela, A. Aboulhorma, Halina Abramowicz, B. S. Acharya, Anke Ackermann, Claire Adam Bourdarios, L. Adamczyk, S. V. Addepalli, Matthew John Addison, J. Adelman, Aytul Adiguzel, T. Adye, Tony Affolder, Y. Afik, M. N. Agaras, Anamika Aggarwal, Catalin Agheorghiesei, None None, A. Ahmad, Faig Ahmadov, S. Ahuja, S. Ahuja, X. Ai, Giulio Aielli, Arya Aikot, Malak Ait Tamlihat, Torsten Akesson, Daiya Akiyama, Nilima Nilesh Akolkar, S. Aktas, Gian Luigi Alberghi, Justin E Albert, Una Helena Alberti, P. Albicocco, S. Alderweireldt, Z. L. Alegria, M. Aleksa, Igor Alexandrov, C. Alexa, Theodoros Alexopoulos, F. Alfonsi, Malte Algren, Muhammad Alhroob, Babar Ali, Hanadi Ali, Shahzad Ali, Samuel William Alibocus, Malik Aliev, Gianluca Alimonti, C. Allaire, B. M. M. Allbrooke, Derrick Allen, Julia Frances Allen, Julia Frances Allen, Julia Frances Allen, E. R. Almazan, Alberto Aloisio, Francisco Alonso, Cristiano Alpigiani, A. Álvarez Fernández, Mario Alves Cardoso, Mariagrazia Alviggi, M. Aly, Y. Amaral Coutinho, Christoph Amelung, M. Amerl, Thiziri Amezza, Baktash Amini, K.J. Amirie, Artem Amirkhanov, Dimitra Amperiadou, Shiwen An, Christos Anastopoulos, Tim Andeen, John Kenneth Anders, Adam Campbell Anderson, A. Andreazza, S. Angelidakis, Aaron Angerami, Alexey Anisenkov, A Annovi, Claire Antel, E. Antipov, Mario Antonelli, Fabio Anulli, Masato Aoki, Takumi Aoki, Marco Aparo, L. Aperio Bella, Mariano Apicella, C. Appelt, A. Apyan, Michaela Arampatzi

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Entanglement is a key property of quantum systems. In this Letter the first measurements of quantum entanglement between spins in pairs of $Z$ 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 $ZZ^*$ spin-density-matrix elements in the $H\rightarrow ZZ^* \rightarrow \ell^+\ell^-\ell^+\ell^-$ process yield coefficients $C_{2,1,2,-1} = -0.71 \pm 0.45$ and $C_{2,2,2,-2}=0.08 \pm 0.44$, 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 $4.9σ$) relative to the entangled Standard Model hypothesis. These results provide strong evidence of quantum entanglement between massive bosons (spin qutrits) at the electroweak scale.

DOI
10.3204/pubdb-2026-01620

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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 $Z$ 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 $ZZ^*$ spin-density-matrix elements in the $H\rightarrow ZZ^* \rightarrow \ell^+\ell^-\ell^+\ell^-$ process yield coefficients $C_{2,1,2,-1} = -0.71 \pm 0.45$ and $C_{2,2,2,-2}=0.08 \pm 0.44$, 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 $4.9\sigma$) 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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Measurements of ZZZ-boson pair entanglement in decays of Higgs bosons at the ATLAS experiment
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.
Measurements of ZZZ-boson pair entanglement in decays of Higgs bosons at the ATLAS experiment
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 4.9σ4.9\sigma4.9σ) relative to the entangled Standard Model hypothesis. These results provide strong evidence of quantum entanglement between massive bosons (spin qutrits) at the electroweak scale.
Entanglement is a key property of quantum systems. In this Letter the first measurements of quantum entanglement between spins in pairs of 𝑍 bosons are reported, using proton-proton collision data from the Large Hadron Collider (LHC) at center-of-mass energies of 13 and 13.6 TeV, recorded with the ATLAS detector. Measurements of angular observables sensitive to 𝑍⁢𝑍* spin-density-matrix elements in the 𝐻→𝑍⁢𝑍*→ℓ+⁢ℓ−⁢ℓ+⁢ℓ− process yield coefficients 𝐶2,1,2,−1=−0.71±0.45 and 𝐶2,2,2,−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 4.9⁢𝜎) relative to the entangled Standard Model hypothesis. These results provide strong evidence of quantum entanglement between massive bosons (spin qutrits) at the electroweak scale.
Entanglement is a key property of quantum systems. In this Letter the first measurements of quantum entanglement between spins in pairs of Z bosons are reported, using proton-proton collision data from the Large Hadron Collider (LHC) at center-of-mass energies of 13 and 13.6 TeV, recorded with the ATLAS detector. Measurements of angular observables sensitive to ZZ^{*} spin-density-matrix elements in the H→ZZ^{*}→ℓ^{+}ℓ^{-}ℓ^{+}ℓ^{-} process yield coefficients C_{2,1,2,-1}=-0.71±0.45 and C_{2,2,2,-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 4.9σ) relative to the entangled Standard Model hypothesis. These results provide strong evidence of quantum entanglement between massive bosons (spin qutrits) at the electroweak scale.
Entanglement is an intrinsic property of quantum mechanics and is predicted to be exhibited in the particles produced at the Large Hadron Collider. A measurement of the extent of entanglement in top quark-antiquark (t¯t) events produced in proton–proton collisions at a center-of-mass energy of 13 TeV is performed with the data recorded by the CMS experiment at the CERN LHC in 2016, and corresponding to an integrated luminosity of 36.3 fb−1 . The events are selected based on the presence of two leptons with opposite charges and high transverse momentum. An entanglement-sensitive observable D is derived from the top quark spin-dependent parts of the t¯t production density matrix and measured in the region of the t¯t production threshold. Values of D < −1/3 are evidence of entanglement and D is observed (expected) to be −0.480+0.026 −0.029 (−0.467+0.026 −0.029) at the parton level. With an observed significance of 5.1 standard deviations with respect to the non-entangled hypothesis, this provides observation of quantum mechanical entanglement within t¯t pairs in this phase space. This measurement provides a new probe of quantum mechanics at the highest energies ever produced.
ATLAS has reported evidence of Z-boson pair entanglement in H → ZZ* → 4ℓ at 4.7σ (4.9σ expected) with 304 fb⁻¹. The separable hypothesis it tests is a single state, the pure product state |00⟩, which ATLAS describes as the only separable state consistent with its assumptions. That is true only for pure states. By ATLAS's own criterion, every state whose two measured coefficients vanish is separable, and that set contains the CP-invariant mixtures of the helicity states |+−⟩, |00⟩ and |−+⟩, not just |00⟩. Restricting the null to |00⟩ therefore presupposes that the spin state is pure, which an entanglement test should not assume. We give a witness built from one event score, Q = (n̂·m̂)², where n̂ and m̂ are the lepton directions in the two Z rest frames. Its mean c lies between 0.32 and 0.36 for every separable two-qutrit state, does not depend on the leptons' analysing power, equals a fixed linear combination of three standard angular coefficients, and gives a tight lower bound on the negativity. In a generator-level model calibrated to the ATLAS result, an ATLAS-style test keeps less than a quarter of its significance when the null is the dephased Standard Model state, which has the Standard Model Z polarizations and no helicity coherence: 1.15σ expected. In this model no test on the same events has an expected significance above 2.4–3.1σ against that state, and the published coefficients give 1.4σ observed evidence of coherence. The witness, valid against every separable state, has an expected significance of 1.8σ (1.6–2.0σ) at 304 fb⁻¹ and 5.6σ (4.9–6.4σ) at 3000 fb⁻¹, from statistics alone. This record includes the paper, its LaTeX source and figures, and the Python scripts, with their outputs, that reproduce every number in it.