Anyonic Entanglement and Topological Entanglement Entropy

Abstract

We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy.

72+13 pages, 37 figures, 2 tables, 2 Easter eggs

References in corpus (14)

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Cited by in corpus (15)

• Anyon condensation and the color code
• A proposal for 3d quantum gravity and its bulk factorization
• Entanglement in tripartitions of topological orders: a diagrammatic approach
• Multipartite edge modes and tensor networks
• Numerical simulation of non-abelian anyons
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• G-crossed Modularity of Symmetry-Enriched Topological Phases
• Topological correlation: anyonic states cannot be determined by local operations and classical communication
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
• Superactivation of Bell nonlocality in pure anyonic states
• Topological entanglement entropy for torus knot bipartitions and the Verlinde-like formulas
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling
• Quantum Resource Theories of Anyonic Entanglement
• Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes
• Entanglement Spectrum Resolved by Loop Symmetries