Remote entanglement stabilization and distillation by quantum reservoir engineering

Quantum information processing in a modular architecture requires the distribution, stabilization and distillation of entanglement in a qubit network. We present autonomous entanglement stabilization protocols between two superconducting qubits that are coupled to distant cavities. The coupling between cavities is mediated and controlled via a three-wave mixing device that generates either a two-mode squeezed state or a delocalized mode between the remote cavities depending on the pump applied to the mixer. Local drives on the qubits and the cavities steer and maintain the system to the desired qubit Bell state. Most spectacularly, even a weakly-squeezed state can stabilize a maximally entangled Bell state of two distant qubits through an autonomous distillation process. Moreover, we show that such reservoir-engineering based protocols can stabilize entanglement in presence of qubit-cavity asymmetries and losses.