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arXiv:2508.14967 · Physical review. D/Physical review. D.

Spin versus nonstabilizerness in gluon and graviton scattering

John Gargalionis, Nathan Moynihan, Sokratis Trifinopoulos, Ewan N. V. Wallace, Chris D. White, Martin J. White

Published Dec 5, 2025• 4 citations
arXivHTMLPDF

Abstract

The quantum property of , also known as , plays a key role in designing quantum computing systems. How to produce, manipulate, and enhance magic remains mysterious, such that concrete examples of physical systems that manifest magic behavior are sought after. In this paper, we study two-particle scattering of gluons and gravitons in Yang-Mills theory and general relativity, as well as their supersymmetric extensions. This provides an interesting case of two-qubit systems, differing only in the physical spin of the qubits. We show that magic is generically produced in both theories, and also show that magic typically decreases as the spin of the qubits increases. The maximal magic in each case is found to be substantially less than the known upper bound. Differences in the profile of magic generation can be traced to the known physics of each theory, as manifested in relations between their respective scattering amplitudes. Our case study may provide useful insights into understanding magic in other systems.

DOI
10.1103/tcb9-3vpr

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The quantum property of , also known as , plays a key role in designing quantum computing systems. How to produce, manipulate, and enhance magic remains mysterious, such that concrete examples of physical systems that manifest magic behavior are sought after. In this paper, we study two-particle scattering of gluons and gravitons in Yang-Mills theory and general relativity, as well as their supersymmetric extensions. This provides an interesting case of two-qubit systems, differing only in the physical spin of the qubits. We show that magic is generically produced in both theories, and also show that magic typically decreases as the spin of the qubits increases. The maximal magic in each case is found to be substantially less than the known upper bound. Differences in the profile of magic generation can be traced to the known physics of each theory, as manifested in relations between their respective scattering amplitudes. Our case study may provide useful insights into understanding magic in other systems.
The property of non-stabiliserness, or ``magic'', is of interest in quantum computing due to its role in developing fault-tolerant quantum algorithms with genuine computational advantage over classical counterparts. There has been much interest in quantifying magic in various physical systems, in order to probe how to produce and enhance it. The production of magic has previously been quantified in gluon and graviton scattering, in the so-called helicity basis relating particle spins with momentum directions. For a basis-independent statement, one should instead use the recently developed concept of non-local non-stabiliserness, and our aim in this paper is to derive how this varies for gluon and graviton scattering processes. Our results show that, for many initial states, including those produced with polarised beams, the helicity basis coincides with a basis in which the non-local magic is manifest, providing a physical motivation for using the helicity basis to study quantum information quantities. However, this property breaks upon adding additional operators to the Yang-Mills Lagrangian, as would be the case in new physics scenarios.
Quantum magic, or nonstabilizerness, is a quantum resource associated with computational advantage in quantum systems. In high energy collisions, Quantum Electrodynamics (QED) is inefficient at generating magic while the weak mixing angle, a fundamental constant of nature, sits near a value that minimizes magic production in charged-lepton scattering. These observations were made in the laboratory (lab) basis, in which spin is projected along the incoming beam axis. An alternative choice is the helicity basis, in which spin is projected along the direction of motion of each particle. The transformation between these two bases is, in general, not a Clifford operation and therefore can change the amount of magic. We present a detailed study of magic production in both bases for QED and electroweak processes, and compare these results with the basis-invariant non-local magic. In the ultra-relativistic limit, magic production is generally smaller in the helicity basis due to helicity selection rules, while the lab basis generally yields less magic in the non-relativistic regime. We provide circuit realizations of the ultra-relativistic Bhabha amplitudes using linear combinations of unitaries and show that the lab basis construction contains a larger TTT-gate count at generic scattering angles. Interestingly, in both bases the physical weak mixing angle lies close to the value that minimizes magic production.
Magic, also known as non-stabilizerness, measures the usefulness of a quantum state for quantum computation. While magic is defined relative to a choice of computational basis, in some physical settings the available data determine this basis only up to local phase conventions. In this paper, we generalize the notion of magic and formulate it in a phase-independent manner, and hence define a generalized stabilizer Rényi entropy. As a case study, we consider higher-multiplicity tree-level gluon scattering, interpreting the outgoing helicities as qubits. In this setting, the helicity data naturally determine a local basis for each qubit but leave a phase ambiguity. For 3→23\to 23→2 scattering, we find that the final-state phase-independent magic is generically larger than the maximum attainable in 2→22\to 22→2 scattering. For 2→32 \to 32→3 scattering, we find a nonzero minimal value approached in the soft limit. Moreover, when the three outgoing momenta become symmetric, the magic approaches a local minimum only a few percent above the soft-limit value. In all cases considered, the color dependence cancels from the phase-independent stabilizer Rényi entropy.
Entanglement is a hallmark of quantum theory, yet it alone does not capture the full extent of quantum complexity: some highly entangled states can still be classically simulated. Non-classical behavior also requires magic, the non-Clifford component that enables universal quantum computation. Here, we investigate whether the interplay between entanglement and magic-state resources constrains the structure of fundamental interactions. We study gluon-gluon and graviton-graviton scattering at tree level. We focus on the high-energy limit, where mass-dependent terms are negligible, and conformal symmetry is preserved. In this regime, all particles behave as massless degrees of freedom, allowing to isolate their transverse helicities as two-qubit states. We explicitly break gauge and general covariance by modifying the quartic vertices and analyzing the resulting generation of entanglement and magic. We find that imposing maximal entanglement (MaxEnt) alone does not uniquely recover gauge-invariant and diffeomorphism invariant interactions, but adding the condition of minimal, but nonzero, magic-state generation singles it out. Our results indicate that nature favors MaxEnt and low magic: maximal quantum correlations with limited non-Cliffordness, sufficient for universal quantum computing but close to classical simulability. This dual informational principle may underlie the emergence of gauge invariance in fundamental physics.
In quantum computing, non-stabilizerness -- the magic -- refers to the computational advantage of certain quantum states over classical computers and is an essential ingredient for universal quantum computation. Employing the second order stabilizer R\'enyi entropy to quantify magic, we study the production of magic states in Quantum Electrodynamics (QED) via 2-to-2 scattering processes involving electrons and muons. Considering all 60 stabilizer initial states, which have zero magic, the angular dependence of magic produced in the final states is governed by only a few patterns, both in the non-relativistic and the ultra-relativistic limits. Some processes, such as the low-energy e−μ−→e−μ−e^-\mu^-\to e^-\mu^-e−μ−→e−μ− and Bhabha scattering e−e+→e−e+e^-e^+\to e^-e^+e−e+→e−e+, do not generate magic at all. In most cases the largest magic generated is significantly less than the maximal possible value of log⁡(16/7)≈0.827\log (16/7) \approx 0.827log(16/7)≈0.827. The only instance where QED is able to generate maximal magic is the low-energy μ−μ+→e−e+\mu^-\mu^+\to e^-e^+μ−μ+→e−e+, in the limit me/mμ→0m_e/m_\mu \to 0me​/mμ​→0, which is well approximated in nature. Our results suggest QED, although capable of producing maximally entangled states easily, may not be an efficient mechanism for generating quantum advantages.
In recent years, there has been increasing collaboration between the fields of quantum computing and high energy physics, including using LHC processes such as top (anti-)quark pair production to perform high energy tests of quantum entanglement. In this proceeding, I will review another interesting property from quantum computing (“magic”), that is needed to make quantum computers with genuine computational advantage over their classical counterparts. How to make and enhance magic in general quantum systems is an open question, such that new insights are always useful. To this end, we will show that the LHC naturally produces magic top quarks, providing a novel playground for further study in this area.