Characterization of the quantum state of top quark pairs produced in proton-proton collisions at $\sqrt{s}$ = 13 TeV using the beam and helicity bases

Measurements of the spin correlation coefficients in the beam basis are presented for top quark-antiquark (𝑡⁢$\overline{𝑡}$) systems produced in proton-proton collisions at √𝑠 =13  TeV collected by the CMS experiment in 2016–2018, and corresponding to an integrated luminosity of 138  fb$^{−1}$. The 𝑡⁢$\overline{𝑡}$ system is reconstructed from final states containing an electron or muon and jets. Together with the previously reported results in the helicity basis, these measurements are used to decompose the system into the Bell and spin eigenstates in various kinematic regions. The spin correlation coefficients are also used to evaluate properties of the 𝑡⁢$\overline{𝑡}$ quantum state, such as the purity, von Neumann entropy, and entanglement. All results are consistent with standard model predictions.