Testing Bell Inequalities at the LHC with Top-Quark Pairs

Correlations between the spins of top-quark pairs produced at a collider can be used to probe quantum entanglement at energies never explored so far. We show how the measurement of a single observable can provide a test of the violation of a Bell inequality at the 98% C.L. with the statistical uncertainty of the data already collected at the Large Hadron Collider, and at the 99.99% C.L. with the higher luminosity of the next run. Detector acceptance, efficiency, and migration effects are taken into account. The test relies on the spin correlations alone and does not require the determination of probabilities—in contrast to all other tests of Bell inequalities.

Figure 1

Kinematics and coordinate systems used in the analysis. The $t$ and $\overline{t}$ rest frames are reached from the $t\overline{t}$ center of mass frame by rotation-free boosts.

Figure 2

Values of the observable $m_1+m_2$ in the phase space of the invariant mass $m_{t\overline{t}}$ vs the scattering angle $\mathrm{\Theta }$. The last bins in $m_{t\overline{t}}$ include overflow events. Bins in the upper right corner have the largest values of $m_1+m_2$ and are selected for testing the violation of the Bell inequality.