Measurements of top quark properties in CMS: $t\bar{t}$ spin density matrix, quantum entanglement and quantum magic

TL;DR

This CMS study uses Run 2 data to probe quantum foundations in $t\overline{t}$ production by (i) extracting the full spin density matrix in the lepton+jets channel via 15 coefficients $Q_m$, (ii) observing entanglement at production threshold and at high $m(t\overline{t})$ through the $D$ and $\tilde{D}$ observables with significances up to $6.7\sigma$, and (iii) performing the first TeV-scale measurement of quantum magic with $\tilde{M}_2$ in $t\overline{t}$, along with complementary dilepton-channel entanglement results. Across channels, the measurements agree with SM predictions and demonstrate collider capability to explore quantum-information concepts in unstable, high-energy systems. The work bridges quantum information science and high-energy physics, illustrating how entanglement and other quantum observables can be accessed in $t\overline{t}$ processes at the LHC.

Abstract

Polarization and spin correlation measurements of top quark-antiquark ($t\bar{t}$) pairs provide tests of the standard model, but also new ways to test quantum mechanics with unstable particles at highest energies ever produced in a laboratory. Recent $t\bar{t}$ spin correlation measurements and the tests they enable, made with the CMS detector at the CERN LHC Run 2, are presented. The measurements summarized include the full spin density matrix measurement of top quark pairs using events with a single lepton and jets in the final state. Spin correlation measurements in specific phase space regions allow the observation of the entanglement phenomenon, and the measurement of quantum magic. From the measured spin correlation at the $t\bar{t}$ production threshold and high $t\bar{t}$ mass, entanglement is observed with a large fraction of the $t\bar{t}$ decays being spacelike separated. The observation of entanglement in $t\bar{t}$ events with two high transverse momentum leptons of opposite charge is also presented. Finally, the first TeV-scale experimental measurement of quantum magic, an important variable for the characterization of quantum states in quantum information science, is presented. These measurements provide one of the first connections between quantum information science and particle physics, and show the potential of collider experiments in the studies of the foundations of quantum mechanics.

Figures (5)

• Figure 1: Measured coefficients of the full matrix for m($t\overline{t}$) $>800~\text{GeV}$ and $\lvert\cos\theta\rvert<0.4$. The data are shown with the statistical uncertainty (inner error bars) and total uncertainty (outer error bars) and compared to the predictions. In the right panel, results are presented with the Powheg+pythia8 predictions subtracted. The Powheg+pythia8 prediction is displayed with QCD scale and PDF uncertainties. Figure taken from Ref. CMS:2024zkc.
• Figure 2: Measurements of $D$ in bins of m($t\overline{t}$) and p$_\text{T}$(t) shown with statistical (inner error bars) and total uncertainty (outer error bars) are compared to various predictions. In the lower panel, the results are presented with the Powheg+pythia8 predictions subtracted. The Powheg+pythia8 predictions are displayed with QCD scale and PDF uncertainties. Figures taken from Ref. CMS:2024zkc.
• Figure 3: The observed levels of entanglement ($\Delta_E$) are displayed in the $t\overline{t}$ threshold region using the $D$ measurement (first bin), and in the high-m($t\overline{t}$) region using the full matrix measurement (second bin). The data are shown with the statistical uncertainty (inner error bars) and total uncertainty (outer error bars) and compared to the predictions including and excluding the $\eta_t$ state. The prediction without $\eta_t$ is displayed with the QCD scale and PDF uncertainties. The horizontal dashed blue lines indicate the maximum level of entanglement $\Delta_{E,crit}$ that can be explained by the exchange of information between $t$ and $\bar{t}$ at the speed of light. Figure taken from Ref. CMS:2024zkc.
• Figure 4: Results of $\tilde{M}_2$ measurements compared to the predictions from various simulation configurations. The measurements are made in bins of m($t\overline{t}$) (upper left), m($t\overline{t}$) with $\lvert\cos\theta\rvert<0.4$ (upper right), and p$_\text{T}$(t) (lower). The Powheg+pythia8 predictions are displayed with the QCD scale and parton distribution function uncertainties, while for all other predictions only the central values are displayed. Figures taken from Ref. CMS:2025cim.
• Figure 5: Measurements of $D$ (black filled or open point) compared with the predictions from simulations including (solid line) or not including (dashed line) the $\eta_t$ state contributions. The predictions without the $\eta_t$ state is shown with $\cancel\eta_t$. Inner (outer) error bars represent the statistical (total) uncertainty for data. The statistical uncertainty in the predictions is shown by the light shaded region and the total uncertainty, including scale and parton distribution function uncertainties, is represented by the darker shaded region. The boundary for entanglement is indicated by the shaded region at high values of $D$. Figure taken from Ref. CMS:2024pts.