Entangled Z Bosons at the LHC: What 4.7 Sigma Actually Rules Out
ATLAS has published strong evidence that the two Z bosons produced in a Higgs decay are entangled, rejecting an unentangled alternative at 4.7 sigma. The result is solid, and ATLAS calls it the first measurement of entanglement between massive force carriers. But the 4.7 sigma rules out one specific unentangled state under Standard Model assumptions, and the direct measurement is not significant on its own. This is what was measured, what it rules out, why it is not a Bell test, and what CMS and the critics say.
Two Z bosons born in a Higgs boson decay share one spin state that cannot be split into two. ATLAS published that claim in Physical Review Letters on 11 September 2026, backed by a 4.7 sigma hypothesis test. It is the first peer-reviewed result on Z boson entanglement. ATLAS calls it the first measurement of entanglement between two massive force carriers. The number holds up. What it rules out is narrower than the coverage suggests, and that gap is the interesting part.
What ATLAS measured
ATLAS looked at Higgs bosons that decay into two Z bosons. Each Z then decays into an electron pair or a muon pair. The data combine the LHC’s full second run with part of its third. That is 140 inverse femtobarns at 13 TeV from 2015 to 2018, plus 164 at 13.6 TeV from 2022 to 2024. Inverse femtobarns measure how much collision data a detector has recorded.
The channel is rare. About one Higgs boson in 8,000 ends as four electrons or muons. It is also unusually clean. ATLAS measures every final particle precisely, and few other processes mimic the signature. Physicists call it the golden channel. It was one of the two decays that revealed the Higgs in 2012.
The paper reports two separate results on Z boson entanglement. The first is a direct measurement of two numbers that describe how the Z spins correlate. The second is a hypothesis test that pits the Standard Model’s entangled prediction against one specific unentangled alternative. The 4.7 sigma headline comes from the second. They answer different questions, so this article takes them one at a time.
Why the Standard Model predicts Z boson entanglement
The Higgs boson has spin zero. The Z boson has spin one. Along any chosen axis, a Z can sit in one of three spin states, labelled +1, 0 and −1. Physicists call a three-level quantum system a qutrit, the three-state cousin of the qubit.
Spin has to balance. The two Z bosons fly apart back to back. Their spins along that line must cancel, to match the Higgs. Three combinations do that: plus with minus, zero with zero, and minus with plus. The Standard Model does not pick one. It predicts a superposition of all three:
|ZZ⟩ = a|+−⟩ + b|00⟩ + c|−+⟩
No single Z state multiplied by another single Z state can reproduce this. That is what entanglement means here. Neither Z has a spin state of its own. Only the pair does.
One more detail matters later. The Higgs weighs about 125 GeV, less than twice the Z mass of 91 GeV. So at least one Z is always virtual, lighter than a real one. Physicists write it Z*. The analysis treats it as a qutrit too. Its decay leptons are highly relativistic, and in that limit the Standard Model gives it the same three spin states.
How four leptons reveal two spins
No detector sees a Z boson’s spin directly. A Z lives about 3 × 10−25 seconds. In that time, light crosses less than a tenth of the width of a proton. The Z never reaches the detector. Its decay products do.
The weak force is chiral: it treats left-handed and right-handed particles differently. Because of that, the direction in which a Z emits its negative lepton depends on the Z’s spin state. Measure that direction in the Z’s own rest frame, over many decays, and the pattern of angles encodes the spin.
ATLAS does this for both Z bosons in every event. It sets a shared axis along the direction of the Z whose mass sits closer to the nominal value, as seen from the Higgs rest frame. For each negative lepton it records a polar angle θ from that axis and an azimuthal angle φ around it. Products of spherical harmonics in those four angles then estimate specific entries of the spin density matrix. That 9 × 9 table fully describes the state of two qutrits.
The step from angles to spins is where theory enters. It assumes each Z decays exactly as the Standard Model says. That assumption carries weight later in the argument.
How ATLAS reads the spins of two Z bosons
Two coefficients, neither significant on its own
The direct result is two numbers, each an average over events:
C2,1,2,−1 = −0.71 ± 0.45 (Standard Model: −0.97)
C2,2,2,−2 = 0.08 ± 0.44 (Standard Model: 0.64)
These coefficients fix the off-diagonal entries of the spin density matrix. Those entries link |00⟩ to |+−⟩, and |+−⟩ to |−+⟩. The paper applies the Peres-Horodecki criterion, a standard test for separability. For this system it gives a clean rule: the pair is entangled if and only if at least one coefficient differs from zero.
Neither coefficient sits far enough from zero to claim that. By this article’s arithmetic, the first is about 1.6 standard deviations from zero. The second is compatible with zero and about 1.3 standard deviations below its prediction. Both agree with the Standard Model. The uncertainties are almost entirely statistical. The angular distributions are broad, and pinning down the average of a broad distribution takes many events.
So the direct route is consistent with entanglement but does not establish it. ATLAS says as much: the paper notes that the spread of the angular distributions limits the precision current data can reach.
What the 4.7 sigma test rules out
The headline number comes from a sharper tool. Instead of averaging, ATLAS fits the full shape of the C2,2,2,−2 distribution. It then asks which of two hypotheses describes the data better.
The first hypothesis is the Standard Model and its entangled superposition. The second is a separable pair with both Z bosons longitudinally polarised: the |00⟩ state alone, with nothing mixed in.
Why that alternative? Under the paper’s assumptions it is the only separable option. Earlier measurements show the Higgs behaves as a CP-even scalar, and the analysis assumes it is one. A lone |+−⟩ or |−+⟩ pair would break CP symmetry. That leaves |00⟩ as the one unentangled state to test.
ATLAS also splits events by the mass of the lighter Z, below and above 30 GeV. A |00⟩ pair would produce a lighter second Z on average, so the mass spectrum carries information too. The paper calls it an indirect probe of entanglement. The split improves the rejection by about 15 per cent.
The test ran 10 million simulated experiments for each hypothesis, with every systematic uncertainty included. The data reject the |00⟩ hypothesis at 4.7 standard deviations. The expected figure, if the Standard Model is right, was 4.9.
What 4.7 sigma does and does not mean
It means a purely longitudinal, unentangled Z pair fits the data very badly, given a scalar Higgs and Standard Model Z decays. It does not mean ATLAS measured entanglement directly. It falls short of the 5 sigma convention for an observation, which is why ATLAS calls it strong evidence. And it says nothing about theories outside quantum mechanics, because the test never included them.
CMS sees the same pattern in a preliminary analysis
CMS released its own study of Z boson entanglement in the same decay in November 2025 and presented it at the Moriond conference in March 2026. It is still a Physics Analysis Summary. That means it has not been through journal peer review.
CMS used 138 inverse femtobarns at 13 TeV and 62 at 13.6 TeV. Its method differs from ATLAS’s. It applies matrix-element techniques to the full kinematics of each event and fits two parameters: the fraction of longitudinal polarisation and a coherence parameter. The Standard Model predicts a longitudinal fraction of 0.61.
CMS excludes both extremes, purely longitudinal and purely transverse Z pairs, at more than 6 standard deviations. Assuming quantum mechanics and CP conservation, it concludes that the pair forms an entangled state of qutrits.
It also tested a subtler quantum effect. With four electrons or four muons, nobody can tell which leptons came from which Z, and the two possible pairings interfere. The data disfavour a model without that interference at 2.7 standard deviations.
The 6 sigma and 4.7 sigma figures are not directly comparable. They come from different methods, different inputs and different stages of review.
Why this is not a Bell test
A Bell test asks a harder question than entanglement does. It asks whether any theory in which particles carry pre-set local properties could produce the observed correlations. Answering it requires experimenters to choose what to measure on each side, freely, after the particles separate.
None of that happens at the LHC. Nobody chooses a measurement setting. The decay itself fixes the lepton directions, and the detector records their momenta afterwards. Physicists then infer the spin information from those momenta, using the Standard Model’s description of the decay.
Both collaborations accept this. In a footnote, ATLAS states that its paper does not test alternatives to quantum mechanics through Bell inequalities. Its aim is narrower: to establish that the Z spin states are non-separable. CMS writes plainly that it cannot perform a true Bell test. It does compute a Bell-type quantity, but only with an extra assumption about coherence. Even then, its allowed range, roughly −0.1 to 2.8, straddles the local limit of 2. Neither experiment claims a violation.
Critics say colliders cannot prove entanglement either
Some theorists go further. Steven Abel, Herbi Dreiner, Rhitaja Sengupta and Lorenzo Ubaldi argue that colliders cannot give an unconditional proof of entanglement either. Their paper appeared in the Journal of High Energy Physics in August 2026.
Their argument turns on what a collider records. It measures only the momenta of final-state particles, and momenta all commute: nature allows all of them to take definite values at once. Using a construction that dates to 1971, the authors build a local hidden-variable model that reproduces such data exactly. The model is separable by design. If an unentangled model can fit the data, the data alone cannot prove entanglement.
A companion preprint by Philip Bechtle, Cedric Breuning, Dreiner and Claude Duhr reaches the same conclusion. It also makes a point that matters for reading ATLAS fairly. Its no-go argument does not apply to entanglement-inspired observables used as tests of the Standard Model.
That is close to what ATLAS actually claims. Its statement is conditional: given quantum mechanics, a scalar Higgs and Standard Model Z decays, the Z spins are not separable. Read that way, the dispute is mostly about what the word entanglement should mean in a headline. CMS cites both critiques in its own analysis.
Three errors in the coverage
Spooky action at a distance. Einstein’s phrase was about nonlocality, the property a Bell test probes. This result does not test it, and neither collaboration says it does.
Entanglement survived the collision. The Z pair does not exist during the proton collision. The collision makes a Higgs boson. The entangled pair appears only when the Higgs decays, and it lasts about 3 × 10−25 seconds.
Three per cent of Higgs decays. ATLAS’s own public briefing attaches this figure to the four-lepton process. It is actually the rate for a Higgs decaying to two Z bosons in any final state. The four-lepton rate is about 1.25 × 10−4, roughly 1 in 8,000.
Several reports also call this one of the highest-energy confirmations of entanglement. That is true but misses the point. The 2024 top-quark result worked with quark pairs of 340 to 380 GeV, well above the 125 GeV Higgs. What is new here is the particles: force carriers with spin one, and three-level systems instead of two.
What the result settles, and what it leaves open
Some of this is settled. ATLAS rejects a separable, purely longitudinal Z pair at 4.7 sigma, given a scalar Higgs and Standard Model Z decays. The spin correlations match the entangled prediction, and the paper has passed peer review.
What to call that is still argued over. One reading sees evidence of Z boson entanglement. The other, set out in published theory work, sees only that the Standard Model’s entangled description fits. Both sides accept the same numbers. They disagree about what the numbers can prove.
More data will sharpen the picture. ATLAS used only part of the LHC’s third run, and the High-Luminosity LHC, expected from mid-2030, aims for ten times the LHC’s design luminosity. New physics in the Higgs couplings would shift these correlations, so they could become a precision probe of the Higgs itself.
No amount of data will make this a Bell test, because nobody at a collider chooses what to measure. What the LHC can do is quieter, and still remarkable. It can check the Standard Model’s quantum description on particles that live about 10−25 seconds and are born from the Higgs. That is not spooky action at a distance. It is a new way to question the Higgs, and it has only just begun.
Note on sourcing
ATLAS figures come from the peer-reviewed Physical Review Letters paper, not from press coverage. The CMS result is preliminary and not yet peer-reviewed. The Abel et al. critique is peer-reviewed; the Bechtle et al. paper is a preprint. The four-lepton branching fraction is the LHC Higgs Cross Section Working Group value. The Z lifetime follows from its measured width of 2.4955 GeV. The stand-alone significances for the two coefficients are this article’s own arithmetic.
References
- ATLAS Collaboration, Measurements of Z-boson pair entanglement in decays of Higgs bosons at the ATLAS experiment, Physical Review Letters 137, 111804 (2026) doi:10.1103/y1nh-1b82
- CMS Collaboration, Study of spin correlations in Higgs boson decays to four leptons at CMS, CMS-PAS-HIG-25-011 (2025), preliminary, not peer-reviewed
- ATLAS Collaboration, Observation of quantum entanglement with top quarks at the ATLAS detector, Nature 633, 542 (2024) doi:10.1038/s41586-024-07824-z
- J. A. Aguilar-Saavedra, A. Bernal, J. A. Casas and J. M. Moreno, Testing entanglement and Bell inequalities in H to ZZ, Physical Review D 107, 016012 (2023) doi:10.1103/PhysRevD.107.016012
- S. A. Abel, H. K. Dreiner, R. Sengupta and L. Ubaldi, Colliders are not testing locality via Bell's inequality nor providing an unconditional proof of entanglement, Journal of High Energy Physics 08 (2026) 067 doi:10.1007/JHEP08(2026)067
- P. Bechtle, C. Breuning, H. K. Dreiner and C. Duhr, A critical appraisal of tests of locality and of entanglement versus non-entanglement at colliders, preprint arXiv:2507.15947 (2025)
Common questions
What did ATLAS find about Z boson entanglement?
ATLAS found strong evidence that the two Z bosons produced when a Higgs boson decays are entangled. A hypothesis test rejected an unentangled pair, with both Z bosons longitudinally polarised, at 4.7 standard deviations. The result assumes a scalar Higgs and Standard Model Z decays, and it appeared in Physical Review Letters in September 2026.
Why is it called strong evidence rather than an observation?
Particle physics reserves the word observation for results at 5 standard deviations or more. At 4.7 standard deviations this result sits just below that line. The two coefficients ATLAS measured directly are not significant on their own.
How can anyone measure the spin of a particle that decays almost instantly?
A Z boson lives about 3 times 10 to the power -25 seconds, so no detector sees it. Physicists infer its spin from the directions of the electrons or muons it decays into. Because the weak force is chiral, those directions depend on the Z spin state, as described by the Standard Model.
Is this a Bell test of quantum nonlocality?
No. A Bell test needs experimenters to choose measurement settings freely after the particles separate, which is impossible at a collider. ATLAS says its paper does not test alternatives to quantum mechanics, and CMS says it cannot perform a true Bell test.
Did CMS find the same thing?
CMS excludes purely longitudinal and purely transverse Z pairs at more than 6 standard deviations and concludes the pair is entangled, assuming quantum mechanics and CP conservation. Its analysis is a preliminary Physics Analysis Summary that has not yet passed peer review. The two significances come from different methods and are not directly comparable.
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