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Universal Lower Bound on Topological Entanglement Entropy.

Isaac H Kim1, Michael Levin2, Ting-Chun Lin3,4

  • 1Department of Computer Science, University of California, Davis, California 95616, USA.

Physical Review Letters
|November 5, 2023
PubMed
Summary
This summary is machine-generated.

Topological entanglement entropy (TEE) in 2D gapped systems has a spurious, non-negative contribution. This finding establishes the anyon theory prediction as a universal lower bound for TEE, enabling a circuit-invariant definition.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Topological Phases of Matter

Background:

  • Two-dimensional gapped ground states are characterized by entanglement entropies obeying an area law.
  • A constant correction term, the topological entanglement entropy (TEE), often reflects the universal properties of the topological phase.
  • The TEE is known to vary even for states within the same phase if they are related by constant-depth quantum circuits.

Purpose of the Study:

  • To investigate the nature of the "spurious" topological entanglement entropy.
  • To determine if the TEE predicted by anyon theory serves as a universal lower bound.
  • To develop a definition of TEE that is invariant under constant-depth quantum circuits.

Main Methods:

  • Analysis of entanglement entropies in two-dimensional gapped ground states.
  • Theoretical investigation of the difference between calculated TEE and anyon theory predictions.
  • Formulation of a modified TEE definition invariant under constant-depth circuit transformations.

Main Results:

  • The spurious contribution to the topological entanglement entropy is proven to be always non-negative.
  • The value predicted by anyon theory provides a universal lower bound for the topological entanglement entropy.
  • A new definition of TEE is proposed, which remains invariant under constant-depth quantum circuits.

Conclusions:

  • The non-negativity of spurious TEE solidifies the anyon theory prediction as a fundamental lower bound.
  • This work reconciles the apparent non-universality of TEE with the underlying topological order.
  • The proposed invariant TEE definition offers a more robust characterization of topological phases.