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

• URL: http://arxiv.org/abs/2606.11296v2
• Date: Tue, 16 Jun 2026 10:58:58 GMT
• Title: Tripartite Entanglement in $e^+ e^- \to t \bar{t} Z$
• Abstract summary: Multipartite entanglement is a uniquely quantum form of correlation that captures collective properties of a composite quantum state.<n>We investigate this phenomenon in the process $e+e-to tbar tZ$ at a future lepton collider.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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