Anyonic Entanglement and Topological Entanglement Entropy
arXiv:1706.09420 · doi:10.1016/j.aop.2017.07.018
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.
arXiv comment72+13 pages, 37 figures, 2 tables, 2 Easter eggs
References in corpus (46)
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Anyons in an exactly solved model and beyond
- Entanglement Entropy and Quantum Field Theory
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Quantum Spin Liquids
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Entanglement entropy and conformal field theory
- String-net condensation: A physical mechanism for topological phases
- Identifying Topological Order by Entanglement Entropy
- Symmetry Fractionalization, Defects, and Gauging of Topological Phases
- Quasi-particle Statistics and Braiding from Ground State Entanglement
- Measurement-Only Topological Quantum Computation
- Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
- Ground state entanglement and geometric entropy in the Kitaev's model
- Entanglement entropy in fermionic Laughlin states
- Entanglement entropy and entanglement spectrum of the Kitaev model
- Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
- Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
- Characterizing topological order by studying the ground states of an infinite cylinder
- Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids
- Three-dimensional topological lattice models with surface anyons
- Topological order in a 3D toric code at finite temperature
- Topological Entanglement Entropy in the Quantum Dimer Model on the Triangular Lattice
- Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
- Bipartite entanglement entropy in fractional quantum Hall states
- Exact Matrix Product States for Quantum Hall Wave Functions
- Interferometry of non-Abelian Anyons
- A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
- Real-Space Entanglement Spectrum of Quantum Hall States
- Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
- Measurement-Only Topological Quantum Computation via Anyonic Interferometry
- Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies
- Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
- Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
- Entanglement entropy of integer Quantum Hall states
- Entanglement signatures of quantum Hall phase transitions
- Topological Entanglement Entropy with a Twist
- Translation invariance, topology, and protection of criticality in chains of interacting anyons
- Long-range entanglement is necessary for a topological storage of quantum information
- Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States
- Entropic Topological Invariants in Three Dimensions
- Ground state entanglement constrains low-energy excitations
- Measures of entanglement in non-Abelian anyonic systems
- Information-theoretical formulation of anyonic entanglement
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- The boundaries and twist defects of the color code and their applications to topological quantum computation
- A proposal for 3d quantum gravity and its bulk factorization
- Realizing topologically ordered states on a quantum processor
- Entanglement in tripartitions of topological orders: a diagrammatic approach
- Multipartite edge modes and tensor networks
- Quantum teleportation using Ising anyons
- Numerical simulation of non-abelian anyons
- Deterministic quantum one-time pad via Fibonacci anyons
- Boundary topological entanglement entropy in two and three dimensions
- Reaction-diffusion dynamics in a Fibonacci chain: Interplay between classical and quantum behavior
- Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
- G-crossed Modularity of Symmetry-Enriched Topological Phases
- Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
- Topological correlation: anyonic states cannot be determined by local operations and classical communication
- Superactivation of Bell nonlocality in pure anyonic states
- Entanglement Spectrum Resolved by Loop Symmetries
- Topological entanglement entropy for torus knot bipartitions and the Verlinde-like formulas
- Quantum Resource Theories of Anyonic Entanglement
- Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling
- Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes