Quantum Information Principles Constrain Gauge Invariance, Revealing Entanglement and Magic’s Role in Fundamental Interactions

Entanglement, a key feature of quantum systems, does not fully explain the complexity observed in nature, as some highly entangled states remain classically simulatable. Claudia Núñez from Institut Cartogràfic, Miguel Pardina, Manuel Asorey, and José Ignacio Latorre, along with Alba Cervera-Lierta, investigate how entanglement and ‘magic’, a property enabling universal computation, shape fundamental interactions. The team examines gluon-gluon and graviton-graviton scattering, deliberately disrupting established gauge and covariance principles by altering interaction strengths, and then analyses the resulting entanglement and magic. Their results demonstrate that requiring maximal entanglement alone fails to uniquely define the expected interactions, but combining this with a principle of minimal, yet non-zero, magic successfully identifies the correct form. This suggests that nature favours systems exhibiting strong correlations with limited complexity, a dual principle that may explain the emergence of gauge invariance in fundamental physics.

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 behaviour also requires magic, the non-Clifford component that enables universal quantum computation. This research investigates whether the interplay between entanglement and magic constrains the structure of fundamental interactions. The study focuses on gluon-gluon and graviton-graviton scattering at tree level, explicitly breaking gauge and general covariance by modifying the quartic vertices and analysing the resulting generation of entanglement and magic. The findings demonstrate that imposing maximal entanglement leads to specific consequences for the observed quantum behaviour in these interactions.

Entanglement Measures and Non-Locality Foundations

Scientists employ a range of measures to quantify entanglement and explore its foundations in quantum mechanics. These tools allow researchers to identify and characterize maximally entangled states, crucial for understanding quantum correlations. Investigations into Bell inequalities demonstrate non-classical correlations and further illuminate the nature of entanglement. A significant emerging theme is the concept of quantum magic, a measure of how far a quantum state deviates from being stabilizable and a key resource for quantum computation. Researchers utilize the stabilizer formalism to characterize quantum states and quantify their properties.

In the realm of particle physics, entanglement plays an increasingly important role. Scientists have observed entanglement in top quark pairs produced at the Large Hadron Collider, providing a direct test of quantum mechanics in a high-energy environment. Investigations explore the possibility of detecting entanglement in Higgs boson decays and in the production of pairs of bosons. Researchers also examine entanglement in decays involving flavored particles, such as B mesons. The Standard Model Effective Field Theory provides a framework for searching for new physics beyond the Standard Model using entanglement as a probe.

Some theoretical work suggests a connection between entanglement suppression and the emergence of symmetries in particle physics. Computational tools, such as FeynCalc and FeynGrav, facilitate the calculation of scattering amplitudes in quantum field theory and gravity. Connections to string theory offer further insights into the nature of gravity. Quantum circuits provide a means to generate and manipulate entangled states. Recent advances include the use of quantum tomography to reconstruct quantum states and the application of quantum magic to quantum electrodynamics and beyond. Entanglement serves as a powerful tool for precision tests of the Standard Model and for searching for new physics. The interplay between quantum information theory and particle physics is growing, with concepts from both fields informing advancements in the other.

Entanglement and Magic Define Fundamental Interactions

Scientists investigated the interplay between entanglement and magic, quantum properties crucial for understanding the structure of fundamental interactions. The research focused on gluon-gluon and graviton-graviton scattering at tree level, deliberately modifying interactions to analyze the resulting generation of entanglement and magic. Results demonstrate that simply maximizing entanglement does not uniquely define the fundamental interactions observed in nature. However, when combined with the condition of minimal, but nonzero, magic, the property enabling universal quantum computation, a unique solution emerges that accurately reflects established interactions.

This work reveals that nature appears to favor maximal entanglement alongside low magic, sufficient for universal quantum computing, yet close enough to classical simulability to avoid complete complexity. Researchers quantified both entanglement and magic using measures appropriate for two-qubit pure states, allowing for a precise analysis of these properties in massless bosons like gluons and gravitons. The team explicitly broke gauge invariance and general covariance by modifying quartic vertices, then examined how these alterations impacted the generation of entanglement and magic. Measurements confirm that enforcing maximal entanglement alone is insufficient to recover the physical interactions, but the addition of minimal magic uniquely singles out the correct gauge-invariant solution.

This suggests a dual informational principle governs fundamental physics, favoring maximal quantum correlation while maintaining a limited degree of non-classicality. The research establishes a connection between the weak mixing angle and minimal magic, with calculations yielding a value of approximately 0. 231, closely aligning with experimental observations. Furthermore, the study shows that while quantum electrodynamics produces almost no magic, top quarks can generate significant magic depending on their kinematics, and gluon-gluon and graviton-graviton scatterings exhibit very low magic at tree level. These findings suggest that quantum information principles, specifically those quantifying entanglement and non-Cliffordness, may play a crucial role in understanding known interactions and searching for physics beyond the Standard Model.

Entanglement, Magic, and Fundamental Interactions Recovered

This research demonstrates a connection between fundamental interactions and the quantum properties of entanglement and magic, or non-classicality. Scientists investigated gluon-gluon and graviton-graviton scattering, deliberately breaking the usual rules of gauge and general covariance to explore how entanglement and magic emerge. The results show that simply maximizing entanglement does not uniquely define the fundamental interactions observed in nature. However, when combined with the principle of minimizing, but not eliminating, magic, the property enabling universal quantum computation, a unique solution emerges that recovers the expected gauge-invariant and diffeomorphism-invariant interactions.

This suggests that nature favors states exhibiting both maximal entanglement and low magic, representing a balance between strong correlations and limited non-classicality. This dual principle may provide insight into the origin of gauge invariance, a cornerstone of modern physics. The authors acknowledge that their analysis is limited to tree-level processes and two-particle interactions, representing a first step towards a more complete understanding. Future research could extend these findings to higher-order processes and more complex interactions, potentially revealing deeper connections between quantum information and the fundamental laws governing the universe.