Genuine Multipartite Entanglement in the Cluster-Ising Model

Abstract

We evaluate and analyze the exact value of a measure for local genuine tripartite entanglement in the one-dimensional cluster-Ising model. This model is attractive since cluster states are considered to be relevant sources for applying quantum algorithms and the Ising interaction is an expected perturbation. Whereas bipartite entanglement is identically vanishing, we find that genuine tripartite entanglement is non zero in the anti-ferromagnetic phase and also in the cluster phase well before the critical point. We prove that the measure of local genuine tripartite entanglement captures all the properties of the topological phase transition. Remarkably, we find that the amount of genuine tripartite entanglement is independent of whether the considered ground states satisfy or break the symmetries of the Hamiltonian. We provide also strong evidences that for this experimentally feasible model local genuine tripartite entanglement represents the unique non vanishing genuine multipartite entanglement among any spins.

7 pages, 4 figures

References in corpus (13)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Identifying Topological Order by Entanglement Entropy
• Measure of genuine multipartite entanglement with computable lower bounds
• Localizable Entanglement
• Genuinely Multipartite Concurrence of N-qubit X-matrices
• Quantum computation on the edge of a symmetry-protected topological order
• Theory of ground state factorization in quantum cooperative systems
• Separability and ground state factorization in quantum spin systems
• Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
• Experimentally Feasible Security Check for n-qubit Quantum Secret Sharing
• Multipartite entanglement measure for all discrete systems
• Enhancement of pairwise entanglement from $\mathbbm{Z}_2$ symmetry breaking
• Macroscopic Observables Detecting Genuine Multipartite Entanglement and Partial Inseparability in Many-Body Systems

Cited by in corpus (6)

• Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction
• Scaling of tripartite entanglement at impurity quantum phase transitions
• Topological and nematic ordered phases in many-body cluster-Ising models
• Genuine multipartite entanglement in a one-dimensional Bose-Hubbard model with frustrated hopping
• Maximally genuine multipartite entangled mixed X-states of N-qubits
• Heuristic for estimation of multiqubit genuine multipartite entanglement