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  • Open Access

Information-Theoretic Principle of Emergent 1-Form Symmetries

Yu-Jie Liu1,2,3,*, Wen-Tao Xu1,2,*, Frank Pollmann1,2, and Michael Knap1,2

  • *These authors contributed equally to this work.
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PRX Quantum 7, 043006 – Published 9 October, 2026

DOI: https://doi.org/10.1103/d6qf-5chk

Abstract

Higher-form symmetries act on subdimensional spatial manifolds of a quantum system. They can emerge as an exact symmetry at low energies even when they are explicitly broken at the microscopic level, making them difficult to characterize. In this work, we propose that the emergence of 1-form symmetries is information-theoretic in nature, characterized by the preservation of information about a specific bare (microscopic) 1-form symmetry. As a consequence, the loss of the emergent 1-form symmetry is an information-theoretic transition which we argue to be revealed from the long-range entanglement in the ensemble of post-measurement states. We analytically determine the regimes in which a 1-form symmetry emerges in product states on one- and two-dimensional lattices. In analytically intractable regimes, we demonstrate how to efficiently detect 1-form symmetries with a global quantum error correction (QEC) decoder and numerically examine the information-theoretic transition of the 1-form symmetry, including systems with Z2 topological order. As a practical application of our framework, we show that once the 1-form symmetry is detected to exist, a topological quantum phase transition characterized by the spontaneous breaking of the 1-form symmetry can be accurately determined by a disorder parameter. We further argue that our proposed theory for emergent 1-form symmetries offers new perspectives on particle condensation and suggests sharp information-theoretic phase boundaries between Higgs and confining regimes in the Z2 lattice gauge theory.

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Popular Summary

Symmetries are a powerful tool for understanding phases of matter. Remarkably, a system can possess symmetries at large length scales that are absent from its microscopic description. Under what conditions can such emergent symmetries exist, and how do they disappear as microscopic perturbations become stronger? In this work, we show how quantum error correction provides a natural framework for understanding and detecting them. Just as error correction recovers information corrupted by noise, it can recover symmetry information obscured by microscopic perturbations. This allows systems with different microscopic details to be recognized as sharing the same emergent symmetry. We develop practical protocols based on this idea, focusing on 1-form symmetries, a class of generalized symmetries important for many quantum phases of matter, including those with topological order. Our approach uncovers surprising hidden symmetry structures within well-known quantum phase diagrams, including sharp transitions at which symmetry information becomes unrecoverable even when no conventional phase transition occurs. These results offer an information-theoretic perspective on emergent symmetries and practical tools for characterizing symmetries and quantum phases.

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PRX Quantum 7, 043006– Published 9 October, 2026
  • Received 24 February 2025
  • Revised 25 June 2026
  • Accepted 16 September 2026
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