Non-Markovian thermal reservoirs as a resource for long-distance entanglement

We describe a novel protocol for the generation of stationary entangled states between two separated qubits that are driven by a common thermal source. Surprisingly, while in this scenario the qubits remain fully separable when the reservoir is broad-band, i.e., Markovian, the steady state of the qubits becomes gradually more entangled as the bandwidth of the thermal source is reduced. We explain this phenomenon by the appearance of a quasi-adiabatic dark state and identify the most relevant non-adiabatic corrections that eventually degrade the entanglement, once thermal fluctuations become too strong. On a general level, the protocol shows how the non-Markovianity of an otherwise incoherent reservoir is transformed into a passive entanglement resource for quantum communication applications in optical, microwave and phononic networks. As a specific example, we discuss the entanglement generation of two scenarios where qubits are driven only by filtered room-temperature noise: two distant superconducting qubits connected by a cryogenic link and a network of spins connected by phononic modes.