The fundamental principles governing how particles interact reveal surprising connections to the quantum world, as demonstrated by research into scattering amplitudes and entanglement. Navin McGinnis from the University of Arizona and colleagues explore the interplay between crossing symmetry, a principle relating different scattering processes, and the creation of quantum entanglement. The team recast scattering amplitudes as operations on quantum systems, revealing that a minimal set of just three fundamental operations spans all possible interactions. This work demonstrates that any interacting field theory exhibiting a global symmetry necessarily generates entanglement in at least one scattering channel, offering new insights into the quantum nature of particle interactions and the emergence of complex behaviour in physical systems.
The results demonstrate that the entire space of SU(N)-invariant scattering operators between qudits is spanned by a minimal set of three quantum gates. Recoupling relations among these gates directly follow from the crossing properties of the underlying amplitudes, revealing that entanglement generated in one scattering channel is necessarily linked to another. Consequently, the team argues that any interacting quantum field theory realizing an SU(N) global symmetry must generate entanglement in at least one scattering channel.
Scattering Amplitudes, Quantum Gates, Entanglement Necessity
This research demonstrates that the space of all possible two-to-two particle scattering amplitudes within local field theories possessing an SU(N) global symmetry is surprisingly simple, being fully described by just three quantum gates: SI, SW, and U. The team recast these scattering amplitudes as operations acting on a ‘qudit’ space, revealing a fundamental connection between particle interactions and quantum information processing. This approach allowed them to establish that any such scattering amplitude can be understood as a manifestation of the cyclic group of order two, a result stemming directly from the underlying principles of crossing symmetry.
Crucially, the analysis shows that crossing symmetry necessitates the generation of entanglement in at least one scattering channel for any theory with the specified symmetry. The researchers found that the relationships between these quantum gates, dictated by recoupling relations, directly mirror the crossing properties of the underlying particle interactions. While the current work focuses on the mathematical structure of these amplitudes, the authors acknowledge that further investigation is needed to fully explore the implications for specific physical systems. Future research will explore the potential of these gates for developing quantum algorithms and will investigate how entanglement predicted by crossing symmetry manifests across different scattering channels.
Scattering Amplitudes, Quantum Gates, Entanglement Necessity
This research demonstrates that the space of all possible two-to-two particle scattering amplitudes within local field theories possessing an SU(N) global symmetry is surprisingly simple, being fully described by just three quantum gates: SI, SW, and U. The team recast these scattering amplitudes as operations acting on a ‘qudit’ space, revealing a fundamental connection between particle interactions and quantum information processing. This approach allowed them to establish that any such scattering amplitude can be understood as a manifestation of the cyclic group of order two, a result stemming directly from the underlying principles of crossing symmetry.
Crucially, the analysis shows that crossing symmetry necessitates the generation of entanglement in at least one scattering channel for any theory with the specified symmetry. The researchers found that the relationships between these quantum gates, dictated by recoupling relations, directly mirror the crossing properties of the underlying particle interactions. While the current work focuses on the mathematical structure of these amplitudes, the authors acknowledge that further investigation is needed to fully explore the implications for specific physical systems. Future research will explore the potential of these gates for developing quantum algorithms and will investigate how entanglement predicted by crossing symmetry manifests across different scattering channels.
👉 More information
🗞 Crossing Symmetry and Entanglement
🧠 ArXiv: https://arxiv.org/abs/2511.10559
