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Separability Transitions in Topological States Induced by Local Decoherence.

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Local decoherence can induce transitions in topological states, making them separable. These transitions align with error correction thresholds, revealing insights into quantum state stability.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Topological Quantum Computing

Background:

  • Topological states of matter possess intrinsic long-range entanglement.
  • Local decoherence can degrade quantum states, impacting their properties.
  • Separability is a key concept for understanding mixed quantum states.

Purpose of the Study:

  • To investigate the effect of local decoherence on topologically ordered states.
  • To determine if decohered states can be represented as ensembles of short-range entangled states.
  • To explore the relationship between decoherence-induced separability and quantum error correction thresholds.

Main Methods:

  • Analysis of toric codes and the X-cube fracton state under local decoherence.
  • Characterization of decohered states using the concept of separability.
  • Connection to Gibbs states and phase transitions in related models (e.g., random bond Ising model).

Main Results:

  • Evidence for decoherence-induced separability transitions in topological states.
  • These transitions coincide with the feasibility threshold for active error correction.
  • Decoherence acting on parent cluster states results in a Gibbs state.

Conclusions:

  • Local decoherence can lead to a transition from topological order to separability.
  • This transition is crucial for understanding the robustness of topological quantum states.
  • The findings provide a new perspective on error correction in topological quantum systems.