https://doi.org/10.1140/epjd/e2017-70671-3
Regular Article
Dynamical matrix for arbitrary quadratic fermionic bath Hamiltonians and non-Markovian dynamics of one and two qubits in an Ising model environment
1 Abdus Salam ICTP, Strada Costiera 11, 34151 Trieste, Italy
2 Departamento de Física – ICEx – Universidade Federal de Minas Gerais, Av. Pres. Antônio Carlos 6627, Belo Horizonte, 31270-901 Minas Gerais, Brazil
3 Universidade Tecnológica Federal do Paraná (UTFPR), Campus Cornélio Procópio, Avenida Alberto Carazzai 1640, Cornélio Procópio, 86300-000 Paraná, Brazil
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e-mail: fernandoiemini@gmail.com
Received: 27 October 2016
Received in final form: 26 January 2017
Published online: 23 May 2017
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.
Key words: Quantum Information
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2017
