Non-local Magic Four Times Anti-Flatness in Two-Particle Scattering Reveals Wavefunction Complexity

The complexity of quantum systems presents a significant challenge to accurate simulation, demanding increasingly powerful computational resources. C. E. P. Robin and M. J. Savage, alongside their colleagues, investigate this complexity through the concepts of non-local magic and anti-flatness, properties that quantify how difficult a quantum state is to reproduce using simple operations. Their work focuses on two-particle scattering processes, specifically low-energy interactions between nucleons and high-energy Moller scattering, revealing a consistent relationship where non-local magic consistently exceeds anti-flatness by a factor of four. Importantly, the team demonstrates that anti-flatness offers a more practical route to experimental measurement, requiring observation of only a single final-state particle and bypassing the need for complex spin correlation analysis, potentially motivating future refinements to experiments such as those conducted at the Thomas Jefferson National Accelerator Facility.

Researchers investigate non-local magic and anti-flatness, measures that quantify the complexity of quantum states and their potential for advanced computation. The team analyses the structure of the scattering wavefunction, quantifying the entanglement generated between colliding particles to understand how these measures evolve during interactions. This approach determines the degree to which the system exhibits quantum advantage, potentially enabling exponential speedups over classical simulation methods.

The study reveals a connection between entanglement measures and the scattering potential, demonstrating how different potential shapes influence the emergence of non-local magic and anti-flatness. These findings contribute a novel understanding of the link between entanglement structure and computational complexity in many-body systems, specifically within scattering processes. The research demonstrates that certain scattering potentials can generate states with significant non-local magic and anti-flatness, suggesting their suitability as resources for universal quantum computation.

Magic, Entanglement and Non-Locality in Scattering Systems

This research provides extensive data and analysis investigating the relationship between magic, entanglement, and non-locality in two distinct physical systems: the nuclear force, observed in proton-proton scattering, and quantum electrodynamics, observed in electron-electron scattering. The core idea is to explore how these quantum resources manifest in different scenarios and whether universal patterns emerge. Researchers utilise stabilizer states as a convenient framework for their analysis, as these states are relatively easy to characterise and manipulate. Magic quantifies the non-classical resources needed to implement a quantum state or process, while entanglement describes the linked fate of two or more particles regardless of distance.

Non-locality refers to correlations that cannot be explained by classical physics. Anti-flatness, closely related to non-locality, acts as a proxy for measuring this phenomenon. The team employs Mandelstam variables and helicity amplitudes to describe the kinematics of the scattering processes. The analysis of proton-proton scattering identifies six groups of stabilizer states based on their behaviour during the interaction. Researchers find that the total linear magic produced is consistent across these groups, regardless of whether the initial states are entangled or not.

However, fluctuations in entanglement differ between groups, indicating varying degrees of disentanglement. The interaction effectively disentangles particles in some groups, leading to structured patterns of non-local magic. Analysis of electron-electron scattering identifies five groups of stabilizer states, with further sub-division in one group. The team finds that entanglement entropy is maximal at a specific scattering angle, consistent with theoretical predictions. However, magic is not maximized at the same angle, indicating a decoupling between entanglement and magic.

The interaction fails to decrease the entanglement of maximally entangled initial states, resulting in no non-local magic being produced, suggesting the generated magic is entirely local. The research reveals system-specific behaviour, with the relationship between magic, entanglement, and non-locality differing between the strong nuclear force and quantum electrodynamics. The decoupling of entanglement and magic in electron-electron scattering suggests that magic can arise from resources beyond entanglement. The study distinguishes between local and non-local magic, with proton-proton scattering exhibiting both types, while electron-electron scattering primarily exhibits local magic.

Disentanglement plays a role in generating non-local magic in proton-proton scattering, suggesting that reducing entanglement can be a useful resource for quantum information processing. These findings have implications for quantum information processing, quantum error correction, and fundamental physics. Understanding the relationship between magic, entanglement, and non-locality is crucial for developing new quantum technologies. Magic is a key resource for quantum error correction, and understanding its origins in different physical systems can improve the design of quantum error-correcting codes. This work contributes to the broader field of resource theories, which aim to quantify the resources needed to perform quantum tasks.

Complexity Link Found in Particle Interactions

This research investigates the generation of quantum complexity in particle interactions, focusing on low-energy nucleon-nucleon scattering and high-energy Moller scattering. Scientists have demonstrated that these processes exhibit quantifiable measures of complexity, termed non-local magic and anti-flatness, which are independent of the chosen measurement basis. The team found a consistent relationship between these two measures, with non-local magic consistently four times greater than anti-flatness, across the studied interactions and initial quantum states. Importantly, anti-flatness is experimentally more accessible, requiring measurement of only one final-state particle’s spin, simplifying potential verification of these findings. The study reveals differences in how quantum electrodynamics and nuclear forces contribute to the generation of non-local magic when starting with maximally entangled particles. The research establishes a clear connection between these complexity measures and the need for quantum computers to accurately simulate complex systems.