The thermal entanglement is investigated in a two-qubit Heisenberg XXZ system with Dzyaloshinskii–Moriya (DM) interaction. It is shown that the entanglement can be efficiently controlled by the DM interaction parameter and coupling coefficient J z . D x (the x -component parameter of the DM interaction) has a more remarkable influence on the entanglement and the critical temperature than D z (the z -component parameter of the DM interaction). Thus, by changing the DM interaction direction, we can get a more efficient control parameter to increase the entanglement and the critical temperature.
We explore the feasibility of realizing Dicke states in qubit arrays with always-on isotropic Heisenberg coupling between adjacent qubits, assuming a single Zeeman-type control acting in the
z direction on an actuator qubit. The Lie-algebraic criteria of controllability imply that such an array is not completely controllable, but satisfies the conditions for subspace controllability on any subspace with a fixed number of excitations. Therefore, a qubit array described by the model under consideration is state-to-state controllable for an arbitrary choice of initial and final states that have the same Hamming weight. This limited controllability is exploited here for the time-efficient dynamical generation of an
a-excitation Dicke state
∣DaN⟩ (
a=1,2,…,N−1) in a linear array with
N qubits starting from a generic Hamming-weight-
a product state. To dynamically generate the desired Dicke states -- including
W states
∣WN⟩ as their special (
a=1) case -- in the shortest possible time with a single local
Z control, we employ an optimal-control scheme based on the {\em dressed chopped random basis} (dCRAB) algorithm. We optimize the target-state fidelity over the expansion coefficients of smoothly-varying control fields in a truncated random Fourier basis; this is done by combining Nelder-Mead-type local optimizations with the multistart-based clustering algorithm that facilitates searches for global extrema. In this manner, we obtain the optimal control fields for Dicke-state preparation in arrays with up to
9 qubits. Based on our numerical results, we find that the shortest possible state-preparation times scale as
O(N2.08) for
W states and
O(N1.78) for
a=2 Dicke states.
This paper investigates the thermal pairwise entanglement of a three-qubit Heisenberg XXZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymmetric interaction and quantum teleportation when using the Heisenberg chain as a channel. The entanglement dependences on the DM interaction and temperature are given in detail. It obtains the relation between the concurrence and average fidelity, and shows that the same concurrence can lead different average fidelities. Moreover, it finds the thermally entangled states which do not violate the Bell inequalities, and can still be used for quantum teleportation.