Witnessing non-Markovian dynamics with the divisibility criterion: a qubit interacting with an Ising model environment
Fernando Iemini, André T. Cesário, Reinaldo O. Vianna · arXiv (Cornell University) · 2015
By means of the divisibility criterion, i.e., the non-positivity of the dynamical matrix for some intermediate time, we characterize the dynamics of a qubit interacting with an arbitrary quadratic fermionic environment. We obtain an analytical expression for the Kraus decomposition of the quantum map, and check its non-positivity with a simple function. With an efficient sufficient criterion to map the non-Markovian regions of the dynamics, we analyze the particular case of an environment described by the Ising Hamiltonian with a transverse field.