Revival structure of the residual entanglement in a three-qubit system

Sammanfattning: The quantum mechanical phenomenon of entanglement plays a key role in areas such as quantum computing and quantum information. Entangled half spin particles, often called qubits, are used to realize quantum based logic which means that studying systems of qubits and their properties is of vital importance to the development of the fields. In this paper we simulate the time evolution of a three-qubit system for varying Hamiltonians and initial states. We look at the revival structure of the classically treated survival probability and compare its structure to that of the quantum mechanical concept of residual entanglement, which is a measure of the system's total entanglement. We do this for three different types of initial states: Uniform, GHZ and W, as well as varying the contributions of certain types of spin-spin interaction models in the Hamiltonian. The spin-spin interaction models that are examined are the DM model and the Heisenberg model. Further we also examine the effect of an added magnetic field in the zdirection, in the form of a Zeeman term. In general, the Zeeman term only affects the behavior of the survival probability, unless the DM term is rotated to not be in a parallel direction, the Heisenberg term generally affects the survival probability and the residual entanglement in the same way. We also note that for the Uniform initial state a dominant Heisenberg seems to remove some of the rapid oscillations in the residual entanglement and survival probability that naturally occur in the DM model, the Zeeman term then reintroduces these high frequencies in the survival probability while not affecting the residual entanglement. For some Hamiltonians we do not see any connection between the revival structure of the survival probability and the residual entanglement, while for some there is a clear connection.