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Mixed-State Topological Order and the Errorfield Double Formulation of Decoherence-Induced Transitions.

Yimu Bao1, Ruihua Fan2, Ashvin Vishwanath2

  • 1University of California, Department of Physics, Berkeley, California 94720, USA.

Physical Review Letters
|June 22, 2026
PubMed
Summary

We developed a theory showing decoherence causes phase transitions in topological quantum states, impacting quantum information protection. These transitions reveal how topological order degrades under noise.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Field Theory

Background:

  • Topological quantum states offer robust quantum information protection.
  • Decoherence is a major challenge for maintaining quantum states.
  • Understanding decoherence effects on topological order is crucial for quantum technologies.

Purpose of the Study:

  • To develop a theoretical framework for decoherence in Abelian topological states.
  • To characterize the impact of decoherence on quantum information protection capacity.
  • To classify decoherence-induced phases and quantum information loss.

Main Methods:

  • Development of an effective field theory.
  • Analysis of decoherence as a temporal defect in a double topological quantum field theory.
  • Classification using Lagrangian subgroups of the double topological order.

Main Results:

  • Decoherence drives boundary phase transitions involving anyon condensation.
  • Identified critical coupling strengths for these transitions.
  • Classified decoherence-induced phases and quantum information loss mechanisms.

Conclusions:

  • The framework generalizes error recovery transitions to generic topological states.
  • Decoherence-induced phase transitions are linked to intrinsic topological order changes in mixed states.
  • Provides a pathway to understand and mitigate decoherence in topological quantum systems.