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

Dorival Gonçalves ^1,*, Alberto Navarro ^2,†, and Kazuki Sakurai ^3,‡

¹Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA
²Institute for Convergence of Basic Studies, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea
³Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland

^*Contact author: dorival@okstate.edu
^†Contact author: alberto.navarro1001@seoultech.ac.kr
^‡Contact author: kazuki.sakurai@fuw.edu.pl

Phys. Rev. D 114, 073004 – Published 23 October, 2026

DOI: https://doi.org/10.1103/l88d-nfqp

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 $H = C^{2} \otimes C^{2} \otimes C^{3}$ . Starting from the standard model helicity amplitudes, we reconstruct the full $12 \times 12$ spin density matrix and characterize 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 polarized lepton collider. By contrast, certifying genuine multipartite entanglement is more challenging, with only limited sensitivity projected for a specific polarization benchmark within the luminosity expected at the International Linear Collider. 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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Phys. Rev. D 114, 073004– Published 23 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 4 July 2026
Accepted 7 October 2026

DOI: https://doi.org/10.1103/l88d-nfqp

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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

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Tripartite entanglement in e+e−→tt¯Z

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