Spin versus Magic: Lessons from Gluon and Graviton Scattering

TL;DR

This paper investigates how quantum 'magic' arises in two-particle gluon and graviton scattering, revealing that magic is common but decreases with increasing spin, offering insights into quantum system design.

Contribution

It demonstrates that magic is generically produced in gluon and graviton scattering and analyzes how it varies with particle spin in different theories.

Findings

Magic is generically produced in both theories.

Magic decreases as the spin of the qubits increases.

Maximal magic is less than the known upper bound.

Abstract

The quantum property of non-stabiliserness, also known as magic, 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 behaviour 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.