Tripartite Entanglement in $e^+ e^- \to t \bar{t} Z$

Abstract

Multipartite entanglement is a uniquely quantum form of correlation that captures collective properties of a composite quantum state beyond those encoded in its bipartite subsystems. We investigate this phenomenon in the process $e^+e^-\to t\bar tZ$ at a future lepton collider, where the final state spins span the tripartite Hilbert space $\mathscr{H}=\mathbb{C}^{2}\otimes\mathbb{C}^{2}\otimes\mathbb{C}^{3}$. Starting from the Standard Model helicity amplitudes, we reconstruct the full $12\times 12$ spin density matrix and characterise its entanglement structure through one-to-one negativities, one-to-other negativities, and the genuine multipartite negativity, evaluated at three increasingly inclusive levels of phase space integration. Pairwise entanglement is generally suppressed relative to the collective (one-to-other) and the genuine multipartite entanglement, and all measures decrease as more kinematic information is integrated out. Assuming quantum tomography in the fully leptonic decay channel at $\sqrt{s}=1$ TeV, we find that the collective entanglement is accessible at a realistic high-luminosity polarised lepton collider, while a direct observation of genuine multipartite entanglement is challenging and would benefit from further optimisation of the event analysis and observable choice. The study establishes $e^+e^-\to t\bar tZ$ as an attractive laboratory for probing multipartite entanglement in high-energy collisions and provides a general mixed state framework that applies to any tripartite spin system.