A theoretical study explores the potential of quantum spin correlations in top-antitop ($t\bar{t}$) pair production at future lepton colliders. The aim is to search for the existence of additional neutral gauge bosons, denoted $Z'$, which arise in extensions of the Standard Model with anomaly-free $U(1)$ symmetries. The research focuses on how the spin-density matrix, including the exchange of photons ($\gamma$), $Z$ bosons, and hypothetical $Z'$ bosons, as well as their interferences, can reveal the presence of these new particles.

The researchers analyzed quantum-information observables such as the sufficient entanglement marker $\mathcal{D}_{\min}$, concurrence, purity, and the maximal Clauser-Horne-Shimony-Holt (CHSH) parameter. These were compared with information obtained from conventional production rates. Different charge assignments within the $U(1)_X$ framework were considered to investigate how chiral structures influence these observables, with particular emphasis on the $Z'$ resonance region and polarized $e^-e^+$ collisions.

Electron-beam polarization provides a direct handle on the left- and right-handed lepton charges in various $U(1)_X$ scenarios. The results suggest that quantum spin observables provide information complementary to cross sections and angular distributions in searches for chiral neutral gauge interactions. This is crucial for identifying and characterizing potential $Z'$ bosons that could mediate fundamental forces yet unknown.