Multipartite entanglement of the topologically ordered state in a perturbed toric code

Abstract

We demonstrate that multipartite entanglement, witnessed by the quantum Fisher information (QFI), can characterize topological quantum phase transitions in the spin-$\frac{1}{2}$ toric code model on a square lattice with external fields. We show that the QFI density of the ground state can be written in terms of the expectation values of gauge-invariant Wilson loops for different sizes of square regions and identify ${\mathbb{Z}}_2$ topological order by its scaling behavior. Furthermore, we use this multipartite entanglement witness to investigate thermalization and disorder-assisted stabilization of topological order after a quantum quench. Moreover, with an upper bound of the QFI, we demonstrate the absence of finite-temperature topological order in the 2D toric code model in the thermodynamic limit. Our results provide insights to topological phases, which are robust against external disturbances, and are candidates for topologically protected quantum computation.

6+4 pages, 3+0 figures

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement detection
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Fisher Information and entanglement of non-Gaussian spin states
• Quench dynamics across quantum critical points
• Entanglement and topological entropy of the toric code at finite temperature
• Entanglement and spin squeezing in non-Hermitian phase transitions
• Multipartite entanglement in topological quantum phases
• Experimental realisation of multipartite entanglement via quantum Fisher information in a uniform antiferromagnetic quantum spin chain
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Fisher information universally identifies quantum resources
• Probing topological order with Rényi entropy
• Quantum Fisher Information as the Convex Roof of Variance
• The Non-Equilibrium Reliability of Quantum Memories
• Protecting topological order by dynamical localization

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• Can multipartite entanglement be characterized by two-point connected correlation functions ?
• Multipartite entanglement structure of monitored quantum circuits
• Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition
• Partially topological phase in a quantum loop gas model with tension and pressure
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits