Gauge invariance from quantum information principles
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Abstract
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 behavior also requires magic, the non-Clifford component that enables universal quantum computation. Here, we investigate whether the interplay between entanglement and magic constrains the structure of fundamental interactions. We study gluon-gluon and graviton-graviton scattering at tree level, explicitly breaking gauge and general covariance by modifying the quartic vertices and analyzing the resulting generation of entanglement and magic. We find that imposing maximal entanglement (MaxEnt) alone does not uniquely recover gauge-invariant and diffeomorphism-invariant interactions, but adding the condition of minimal, but nonzero, magic singles it out. Our results indicate that nature favors MaxEnt and low magic: maximal quantum correlations with limited non-Cliffordness, sufficient for universal quantum computing but close to classical simulability. This dual informational principle may underlie the emergence of gauge invariance in fundamental physics.