Quantum Information meets High-Energy Physics: Input to the update of the European Strategy for Particle Physics

TL;DR

The paper argues for integrating quantum information science with high-energy physics by studying entanglement, Bell nonlocality, and related quantum correlations in collider processes. It describes a methodology based on spin-density matrix reconstruction and quantum state tomography to probe relativistic multipartite states in $t \bar{t}$ production, Higgs decays, and flavor oscillations, while outlining the challenges posed by neutrinos, jet tagging, and Monte Carlo modeling. The work presents a roadmap toward measuring entanglement, discord, steering, and Bell nonlocality across the LHC, HL-LHC, future lepton colliders, and next-generation hadron colliders, highlighting the potential for new physics sensitivity and foundational tests of quantum mechanics. By leveraging collider data and CERN's Quantum Technology Initiative, the approach aims to broaden QIT tools in HEP and accelerate cross-disciplinary advances in both fields.

Abstract

Some of the most astonishing and prominent properties of Quantum Mechanics, such as entanglement and Bell nonlocality, have only been studied extensively in dedicated low-energy laboratory setups. The feasibility of these studies in the high-energy regime explored by particle colliders was only recently shown and has gathered the attention of the scientific community. For the range of particles and fundamental interactions involved, particle colliders provide a novel environment where quantum information theory can be probed, with energies exceeding by about 12 orders of magnitude those employed in dedicated laboratory setups. Furthermore, collider detectors have inherent advantages in performing certain quantum information measurements, and allow for the reconstruction of the state of the system under consideration via quantum state tomography. Here, we elaborate on the potential, challenges, and goals of this innovative and rapidly evolving line of research and discuss its expected impact on both quantum information theory and high-energy physics.

Figures (5)

• Figure 1: Left panel: Quantum discord of $pp \to t \bar{t}$ at the LHC as a function of the top velocity $\beta$ and the production angle $\Theta$ in the $t\bar{t}$ center-of-mass frame. Solid red, dashed-dotted yellow, and dashed brown lines are the critical boundaries of separability, steerability, and Bell locality, respectively Afik:2022dgh. Right panel: The observable ${\cal I}_3$, where ${\cal I}_3 > 2$ implies a Bell nonlocal state, for the process $pp \to Z Z$ as a function of the invariant mass and scattering angle in the center-of-mass energy frame Barr:2024djo.
• Figure 2: Measurement of the entanglement marker $D$, where $D<-1/3$ indicates entanglement. Left panel: ATLAS particle-level $D$ measurement compared with various MC models. Error bars represent all uncertainties included. The entanglement limit shown in the low $m_{t \bar{t}}$ region is a conversion from its parton-level value of $D = -1/3$ to the corresponding value at particle-level ATLAS:2023fsd. Right panel: CMS parton-level $D$ measurement either including (black filled point) or not including (black open point) contribution from toponium, compared to MC predictions with (solid line) or without (dashed line) the inclusion of toponium. Inner error bars represent the statistical uncertainty, while the outer error bars represent the total uncertainty for data CMS:2024pts.
• Figure 3: Left panel: Comparison between two different approaches in the showering algorithm to the simulation of top-quark pair production as a function of the angular variable input to the entanglement witness $D$ calculation ATLAS:2023fsd. Right Panel: Difference with respect to the SM prediction of several terms of the spin density matrix and entanglement witnesses ($\Delta^{+},\Delta^{-}$) in top-quark pair production as a function of a coupling used to parametrize the presence of new physics in the SM vertices. The continuous line is obtained using only leading-order simulations, while the dashed line includes higher-order effects in QCD Severi:2022qjy.
• Figure 4: Left panel: Bell indicator $\mathcal{B}_{1}$ as a function of the luminosity in $pp \to t \bar{t}$ collisions at the LHC and the HL-LHC, where $\mathcal{B}_{1}>0$ implies that the state is Bell nonlocal. The yellow and blue areas represent the regions for an expected statistical significance of $2\sigma$ and $5\sigma$, respectively Dong:2023xiw. Right panel: minimum experimental accuracy estimated to measure Bell nonlocality at $5 \sigma$ in $e^+e^- \to t \bar{t}$ collisions, as a function of the top velocity squared $\beta^2$ and the production angle $\theta$ in the $t\bar{t}$ center-of-mass frame Maltoni:2024csn.
• Figure 5: Left panel: Analytic solution for Bell nonlocality in the parton-level process $e^+ e^- \to \tau^+ \tau^-$. The presence of Bell nonlocality is signaled by $m_{12}>1$. Right panel: Tests of $\chi^2$ in $e^+e^-$ events for the form factor $F_2^V(m_Z^2)$, acting as anomalous coupling of the $\tau$-leptons to the $Z$-boson, using the cross section (blue) and entanglement marker (red), show that the latter provides more stringent limits. Both plots are from Ref. Fabbrichesi:2024wcd.