Some entanglement features exhibited by two, three and four qubits interacting with an environment in a non-Markovian regime

Abstract

We explore various aspects of the quantum entanglement dynamics of systems of two, three and four qubits interacting with an environment at zero temperature in a non-Markovian regime, as described by the paradigmatic model recently studied by Bellomo, Lo Franco, and Compagno [Bellomo et al. Phys. Rev. Lett. 99 (2007) 160502]. We consider important families of initial states for the alluded systems. The average, typical entanglement evolution associated with each of these families is determined, and its relation with the evolution of the global degree of mixedness of the multi-qubit system is explored. For three and four qubits we consider the family of initial states equivalent under local unitary transformations to the jGHZi and jWi states, and compare their average behavior with the average behavior exhibited by initial maximally entangled twoqubits states. Furthermore, in the case of two qubits, the evolution of other manifestations of entanglement, related to measurable quantities, is also investigated. In particular, we consider the Mintert-Buchleitner concurrence lower bound and an entanglement indicator based upon the violation of local uncertainty relations.