Particle Colliders Could Turn High-Energy Debris Into a New Test of Quantum Nonlocality

Particle colliders may soon become laboratories for one of quantum physics’ strangest predictions: Bell non-locality, the phenomenon in which correlations between separated quantum systems cannot be explained by any theory based on local hidden properties. In a new analysis, physicists describe how collisions producing entangled particles could be used to reconstruct their complete quantum states and then test whether those states contain correlations that defy classical explanations. Unlike traditional Bell experiments, which select measurement settings before examining each particle, collider-based studies can use the debris of high-energy collisions to perform quantum state tomography—a mathematical reconstruction of the system’s density matrix. The approach could allow researchers to investigate entanglement and non-locality in environments governed simultaneously by quantum mechanics, the Standard Model of particle physics, and the powerful strong and electroweak interactions.

The work, by M. Fabbrichesi, R. Floreanini and L. Marzola, focuses on a fundamental difference between ordinary laboratory Bell tests and measurements at colliders. In a conventional experiment, a source produces two entangled particles that travel to separate detectors. Investigators choose measurement directions at the two stations, record the outcomes and compare the resulting correlations with a Bell inequality. A violation rules out local hidden-variable models under assumptions about locality, measurement independence and detector behavior. At a collider, however, the particles are not usually measured with adjustable polarimeters. Instead, their spins or polarizations are inferred from the angular and momentum distributions of their decay products. Those distributions encode information about the quantum state created in the collision, allowing physicists to reconstruct the state first and calculate the relevant correlations afterward.

The quantum systems produced in these reactions can include two-level systems known as qubits, such as fermions with spin one-half, as well as three-level systems called qutrits, including massive spin-one bosons. Their quantum state is represented by a density matrix, a mathematical object that contains the probabilities of possible outcomes and the coherence terms linking different possibilities. Quantum tomography estimates the entries of this matrix from many collision events. For a pair of spin-one-half particles, the matrix can be expressed through single-particle polarization vectors and a correlation tensor describing how measurements on one particle are related to measurements on the other. Once these quantities are known, researchers can calculate entanglement measures and evaluate a Bell inequality such as the Clauser–Horne–Shimony–Holt relation. A value beyond the limit allowed by local realism would provide evidence of Bell non-local correlations.

The strategy is particularly powerful because collider events naturally provide many potential measurement axes. A particle’s decay products are not random clutter; their directions are statistically linked to the parent particle’s spin. In a weak decay, for example, parity-violating interactions can make a charged lepton or another daughter particle act as a spin analyser. The direction of that daughter particle becomes a polarimetric vector, carrying information about the orientation of the original spin. By collecting large samples and fitting the multidimensional angular distributions, experiments can determine polarization and spin-correlation coefficients without installing a physical analyzer that must be rotated between settings. In fully leptonic top-quark decays, the chiral structure of the weak interaction can make the charged lepton an especially effective analyzer. Similar principles apply to tau leptons, baryons and vector bosons, although each system has different lifetimes, decay channels and reconstruction challenges.

That difference changes how familiar Bell-test loopholes must be understood. The locality loophole arises when information about a measurement setting could travel from one detector to the other before both outcomes are recorded. In a conventional experiment, researchers address it by separating the measurements in space and choosing detector settings rapidly and independently. Collider experiments often cannot arrange two long-lived particles to decay in perfectly space-like separated regions, and some particles decay at very different distances from the collision point. The analysis argues that this timing problem does not have the same force when the entire state is reconstructed before the Bell correlations are calculated. The directions used in the final mathematical test are not chosen at the production point or during the individual decays. They are selected only after the density matrix has been inferred, so the state cannot have carried advance information about those later choices.

The detection loophole also takes a different form. In photon experiments, an incomplete detector can preferentially record events that happen to support a Bell violation, while unobserved events conceal correlations compatible with local realism. Collider physicists routinely confront missing events, trigger efficiencies and reconstruction biases, but the authors argue that the tomography procedure does not define a subset by choosing favorable measurement directions. Instead, selection criteria are applied to reconstruct the state, and the missing events generally dilute the statistical significance rather than selectively manufacture a non-local correlation. This does not eliminate the need for efficiency studies, background estimates and uncertainty propagation. It means that a proposed loophole based on selectively retaining outcomes associated with particular analyzer settings is difficult to formulate when no analyzer settings exist during data collection.

The freedom-of-choice loophole is similarly reframed. In a standard Bell test, a hidden-variable theory could hypothetically correlate the properties emitted by the source with the later choices made by the experimenters. Such a theory might reproduce quantum-looking correlations if the supposedly independent settings were not genuinely independent. Collider tomography removes the operational role of those choices: the data are acquired through a fixed reconstruction procedure, and the axes used to evaluate the correlations are imposed only after the state has been estimated. The authors connect this point to broader debates about super-determinism, the idea that all apparent choices and hidden variables are correlated through the universe’s initial conditions. They argue that such models would need to explain not merely a selected set of detector settings but the full quantum state and its tomographic reconstruction, while remaining consistent with existing tests of quantum mechanics.

Other possible loopholes receive the same treatment. A memory loophole could allow a local model to use information from earlier settings and outcomes to influence later trials, but collider events arise from separate particle decays occurring at varying positions and times, and the relevant measurement directions are not set event by event in advance. The coincidence loophole, in which a hidden-variable model manipulates detection times so that only favorable pairs are identified as belonging together, is constrained because collider events are paired through their reconstructed kinematics from a common collision. Misidentification remains a real experimental uncertainty, but it is measured and incorporated into the analysis rather than left as an unspecified source of correlations. The authors emphasize that collider tests are not automatically immune to every experimental weakness; their degree of device independence must be evaluated case by case. Their central claim is narrower and more technical: many loopholes that depend on adjustable measurement settings lose their usual mechanism when the quantum state is reconstructed before those settings are defined.

The proposal builds on a rapidly expanding program in particle physics. Experiments at the Large Hadron Collider have already reported quantum entanglement in top-quark pairs, whose spins remain correlated even though the top quark decays almost instantly. The same collider environment could support tests involving tau-lepton pairs, entangled baryons, Higgs-boson decays and massive vector bosons. The systems are attractive because their interactions provide built-in spin analyzers, but they are also difficult: detectors must identify decay products amid enormous backgrounds, account for acceptance effects and reconstruct invisible particles such as neutrinos. Moreover, the density matrix measured across a broad range of collision kinematics may be a weighted mixture of states produced at different scattering angles. If all events are described using one common spatial basis, that mixture can represent a genuine quantum state. If the basis changes from event to event—for example, in a helicity frame—the average may instead describe what the authors call “fictitious states.” Even then, the averaged polarization and correlation coefficients can remain useful for demonstrating that at least some contributing states are entangled or Bell-nonlocal.

The significance of the framework is therefore not that colliders have already delivered a loophole-free Bell test of the kind performed with photons, ions or superconducting circuits. Rather, it supplies a detailed map for turning high-energy collision data into a test of quantum foundations. A successful measurement would probe entanglement where particles are created through fundamental interactions at energies far above those of most quantum-information experiments. It could test whether new particles or unexplained interactions alter the structure of quantum correlations, and it might expose departures from Standard Model predictions through changes in polarization tensors or Bell parameters. The method also provides a bridge between particle physics and quantum information science: the same density matrices used to characterize quantum devices can describe top-quark pairs and bosons born in violent collisions. As future datasets grow, the debris of colliders may offer an unusually energetic stage on which quantum mechanics can confront its most persistent classical alternatives.