Universality of Magic in Local Quantum Field Theory

• URL: http://arxiv.org/abs/2607.16403v1
• Date: Fri, 17 Jul 2026 18:00:12 GMT
• Title: Universality of Magic in Local Quantum Field Theory
• Abstract summary: We show that no stabilizer state in a discrete realization of a local quantum field theory can flow in the continuum to the vacuum or to any state that resembles the vacuum at short distances.<n>Our result implies that simulating physically relevant QFT states necessarily requires quantum resources beyond stabilizer states and Clifford operations.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that no stabilizer state in a discrete realization of a local quantum field theory can flow in the continuum to the vacuum or to any state that resembles the vacuum at short distances. The argument rests on the fact that the entanglement spectrum is flat for stabilizer states but non-flat for cyclic and separating states in a local QFT as a consequence of the type III$_1$ nature of the von Neumann algebras associated with arbitrary subregions. Our result implies that simulating physically relevant QFT states necessarily requires quantum resources beyond stabilizer states and Clifford operations. We comment on the implications for holography.

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