Generating stationary entangled states in superconducting qubits

Abstract

When a two-qubit system is initially maximally entangled, two independent decoherence channels, one per qubit, would greatly reduce the entanglement of the two-qubit system when it reaches its stationary state. We propose a method on how to minimize such a loss of entanglement in open quantum systems. We find that the quantum entanglement of general two-qubit systems with controllable parameters can be controlled by tuning both the single-qubit parameters and the two-qubit coupling strengths. Indeed, the maximum fidelity ${F}_{\text{max}}$ between the stationary entangled state, ${\ensuremath{\rho}}_{\ensuremath{\infty}}$, and the maximally entangled state, ${\ensuremath{\rho}}_{m}$, can be about $2/3\ensuremath{\approx}\text{max}{\text{tr}({\ensuremath{\rho}}_{\ensuremath{\infty}}{\ensuremath{\rho}}_{m})}={F}_{\text{max}}$, corresponding to a maximum stationary concurrence, ${C}_{\text{max}}$, of about $1/3\ensuremath{\approx}C({\ensuremath{\rho}}_{\ensuremath{\infty}})={C}_{\text{max}}$. This is significant because the quantum entanglement of the two-qubit system can be produced and kept, even for a long time. We apply our proposal to several types of two-qubit superconducting circuits and show how the entanglement of these two-qubit circuits can be optimized by varying experimentally controllable parameters.