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arXiv:2608.18732

Genuine Tripartite Entanglement Selects Gauge-Invariant Theories

Junya Yamagishi

hep-phhep-thquant-phSubmitted Aug 19, 2026• Announced Aug 20, 2026• 0 citations
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Abstract

Recent studies have explored whether physical constants and symmetries can be selected by extremizing bipartite entanglement entropy. We extend this approach to a three-particle setting. Specifically, we consider a $2+1$-particle system in which particles $B$ and $C$ are initially entangled, and then particles $A$ and $B$ scatter without the direct participation of particle $C$ for both gluon-gluon and graviton-graviton scatterings. Using angular expansions around the forward and backward scattering limits, we analyze bipartite entanglement in the corresponding two-particle system of $A$ and $B$ and two measures of genuine tripartite entanglement (GTE), the concurrence fill and the generalized geometric measure (GGM), in the three-particle system. As is already known, the bipartite entanglement provides no universal criterion for selecting the symmetry-preserving theory: depending on the initial helicities, it may either maximize or minimize the entanglement entropy. By contrast, we find that the GTE-based analysis uniquely identifies the gauge-invariant and diffeomorphism-invariant theories as those that suppress the GTE in gluon-gluon and graviton-graviton scatterings, respectively. This result suggests a nontrivial connection between tripartite entanglement and the gauge and diffeomorphism symmetries of fundamental interactions.

Comments
29 pages, 5 figures

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Recent studies have explored whether physical constants and symmetries can be selected by extremizing bipartite entanglement entropy. We extend this approach to a three-particle setting. Specifically, we consider a 2+12+12+1-particle system in which particles BBB and CCC are initially entangled, and then particles AAA and BBB scatter without the direct participation of particle CCC for both gluon-gluon and graviton-graviton scatterings. Using angular expansions around the forward and backward scattering limits, we analyze bipartite entanglement in the corresponding two-particle system of AAA and BBB and two measures of genuine tripartite entanglement (GTE), the concurrence fill and the generalized geometric measure (GGM), in the three-particle system. As is already known, the bipartite entanglement provides no universal criterion for selecting the symmetry-preserving theory: depending on the initial helicities, it may either maximize or minimize the entanglement entropy. By contrast, we find that the GTE-based analysis uniquely identifies the gauge-invariant and diffeomorphism-invariant theories as those that suppress the GTE in gluon-gluon and graviton-graviton scatterings, respectively. This result suggests a nontrivial connection between tripartite entanglement and the gauge and diffeomorphism symmetries of fundamental interactions.
From the perspective of quantum information science, we investigate tree-level Bhabha scattering between an incident electron AAA and a positron BBB, where BBB is initially entangled with a spectator electron CCC, which does not participate in the scattering interaction. We find that the quantum electrodynamics (QED) scattering between AAA and BBB can drive the global ABCABCABC system into a genuine tripartite entangled (GTE) state. Using four canonical tripartite entanglement metrics, we systematically characterize and quantify the GTE of the composite system, and demonstrate that the scattering momentum of the AAA-BBB pair and the initial BBB-CCC entanglement are the key resources governing GTE generation. We further analyze the monogamy of quantum correlations, which imposes fundamental constraints on the shareability of quantum resources in multipartite systems. Specifically, we systematically study the monogamy relations for the squared entanglement of formation and squared quantum discord in our scattering model, and find that monogamy constraints are markedly relaxed in the non-relativistic regime, enabling enhanced shareability of quantum correlations across the three particles. This work uncovers novel quantum correlation properties of fundamental QED scattering processes, and provides direct theoretical guidance for the development of QED-based quantum information processing protocols.
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