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Non-local nonstabiliserness in Gluon and Graviton Scattering

John Gargalionis, Nathan Moynihan, Michael L. Reichenberg Ashby, Ewan N. V. Wallace, Chris D. White, Martin J. White

Abstract

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.

Non-local nonstabiliserness in Gluon and Graviton Scattering

Abstract

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.
Paper Structure (7 sections, 59 equations, 4 figures)

This paper contains 7 sections, 59 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Review of necessary background
  3. Non-local magic in $2\rightarrow 2$ scattering
  4. Results
  5. Deforming Yang-Mills theory
  6. Conclusion
  7. Helicity amplitude combinations for different particle species

Figures (4)

  • Figure 1: The non-local magic (red) arising from representative initial stabiliser states from the groups in table \ref{['tab:stabstates']}. Also shown is the local magic in the helicity basis (blue), where this differs from the non-local magic; and the concurrence (dashed).
  • Figure 2: The non-local magic (red) arising from representative initial stabiliser states from the groups in table \ref{['tab:stabstates']}. Also shown is the local magic in the helicity basis (blue), where this differs from the non-local magic; and the concurrence (dashed).
  • Figure 3: (a) The non-local magic power $\overline{\mathcal{M}_{AB}}$ of eq. (\ref{['magpownonlocal']}) as a function of scattering angle $\theta$ and (b) the integrated non-local magic power $\left<\mathcal{M}_{AB}\right>$ of eq. (\ref{['intpow']}) for gluinos, gluons, gravitinos, and gravitons.
  • Figure 4: Final state local (blue) and non-local (red) magic in the helicity basis corresponding to the initial state $\ket{+-}$. Results are shown for the deformed Yang-Mills theory of eq. (\ref{['LF3']}) in (a) as a function of the scaled Wilson coefficient $\tilde{c}$ of eq. (\ref{['ctildedef']}) and scattering angle $\theta$. Cross-sections are shown for particular values of $\tilde{c}$ in (b) and $\theta$ in (c), with the maximum analytic magic values for this scattering process. The section with $\theta=\cos^{-1}\left[ 1+\sqrt 2\left(1-\sqrt{1+\sqrt2}\right)\right]$ corresponds to the maximum non-local magic in the Yang-Mills limit.