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 $e^{+}{e}^{-}\to t\bar{t}Z$ at a future lepton collider, where the final state spins span the tripartite Hilbert space $\mathcal{H}={\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^3$. 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 collective entanglement should be accessible at a realistic high-luminosity polarised lepton collider. By contrast, certifying genuine multipartite entanglement is more challenging, with only limited sensitivity projected for a specific polarisation benchmark within the expected ILC luminosity. The study establishes $e^{+}{e}^{-}\to t\bar{t}Z$ 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.

Figures 4-7 and the associated discussion have been updated