Entanglement statistics of randomly interacting spins

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Abstract
We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can continuously interpolate between deterministic separable eigenstates and fully random entangled eigenstates, with nontrivial intermediate behavior. Entanglement strongly depends on the underlying topology of the interaction among the qubits. Since W states correspond to a zero-measure set as compared to the set of Greenberger-Horne-Zeilinger (GHZ) states, in all investigated cases the ground states are of the latter type. However, for a certain class of interactions (nonseparable collective potential) high GHZ entanglement is produced, while for fully separable pairwise interactions the marginal GHZ ground states concentrate in the vicinity of W states.
Funding Information
  • Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
  • Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco
  • Conselho Nacional de Desenvolvimento Científico e Tecnológico (465469/2014-0, 405508/2021-2)
  • Fundação de Amparo à Pesquisa do Estado de Goiás (2021/06535-0)
  • Fundação de Amparo à Pesquisa do Estado de São Paulo (2021/06535-0)

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