Highly Entangled Ground States in Tripartite Qubit Systems

We investigate the creation of highly entangled ground states in a system of three exchange-coupled qubits arranged in a ring geometry. Suitable magnetic field configurations yielding approximate Greenberger-Horne-Zeilinger and exact W ground states are identified. The entanglement in the system is studied at finite temperature in terms of the mixed-state tangle τ. By generalizing a conjugate gradient optimization algorithm originally developed to evaluate the entanglement of formation, we demonstrate that τ can be calculated efficiently and with high precision. We identify the parameter regime for which the equilibrium entanglement of the tripartite system reaches its maximum.