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Dynamical matrix for arbitrary quadratic fermionic bath Hamiltonians and non-Markovian dynamics of one and two qubits in an Ising model environment

  • Fernando IeminiEmail author
  • Leonardo da Silva Souza
  • Tiago Debarba
  • André T. Cesário
  • Thiago O. Maciel
  • Reinaldo O. Vianna
Regular Article

Abstract

We obtain the analytical expression for the Kraus decomposition of the quantum map of an environment modeled by an arbitrary quadratic fermionic Hamiltonian acting on one or two qubits, and derive simple functions to check the non-positivity of the intermediate map. These functions correspond to two different sufficient criteria for non-Markovianity. In the particular case of an environment represented by the Ising Hamiltonian, we discuss the two sources of non-Markovianity in the model, one due to the finite size of the lattice, and another due to the kind of interactions.

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Keywords

Quantum Information 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Fernando Iemini
    • 1
    Email author
  • Leonardo da Silva Souza
    • 2
  • Tiago Debarba
    • 3
  • André T. Cesário
    • 2
  • Thiago O. Maciel
    • 2
  • Reinaldo O. Vianna
    • 2
  1. 1.Abdus Salam ICTPTriesteItaly
  2. 2.Departamento de Física – ICEx – Universidade Federal de Minas GeraisMinas GeraisBrazil
  3. 3.Universidade Tecnológica Federal do Paraná (UTFPR)ParanáBrazil

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