Entanglement distillation between solid-state quantum network nodes

Abstract

The potential impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable real-world imperfections necessitate means to improve remote entanglement by local quantum operations. Here we realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. We demonstrate the heralded generation of two copies of a remote entangled state through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements herald the distillation of an entangled state with increased fidelity that is available for further use. In addition, this distillation protocol significantly speeds up entanglement generation compared to previous two-photon-mediated schemes. The key combination of generating, storing and processing entangled states demonstrated here opens the door to exploring and utilizing multi-particle entanglement on an extended quantum network.Future quantum networks connecting nodes of longlived stationary qubits through photonic channels may enable secure communication, quantum computation and simulation, and enhanced metrology [1][2][3][4][5][6][7][8][9]. The power of these applications fundamentally derives from quantum entanglement shared between the network nodes. The key experimental challenge is therefore to establish high-quality remote entanglement in the presence of unavoidable errors such as decoherence, photon loss and imperfect quantum control. Remarkably, by only using classical communication and local quantum operations, a high-fidelity remote entangled state can be distilled from several lower-fidelity copies [10,11] (Fig. 1A). Success of this intrinsically probabilistic distillation can be nondestructively heralded by measurement outcomes such that the distilled state is available for further use, a critical requirement for scalable networks. Owing to these unique features, entanglement distillation, also known as purification, has become a central building block of quantum network proposals [6-9, 12, 13]. GENERATION AND DISTILLATION OF REMOTE ENTANGLED STATESTo run entanglement distillation on a quantum network, several copies of a raw entangled state must first be shared between the nodes. This can be achieved using a network primitive of two nodes with two qubits * These authors contributed equally.† Present address: Max-Planck-Institute for Quantum Optics, Hans-Kopfermann-Str. 1, 85748 Garching, Germany ‡ To whom correspondence should be addressed; E-mail: r.hanson@tudelft.nl each: a communication qubit with an optical interface for generating remote entanglement and a memory qubit for storage (Fig. 1B). First the communication qubits run the entangling protocol, which due to photon loss is intrinsically probabilistic. After photon detection heralds the generation of a raw entangled state on the communication qubits, this state is swapped onto the memory qubits. The communication qubits are then used to generate a...

Quantum Networks with Deterministic Spin–Photon Interfaces

“…If the ground state of the quantum emitter consists of a coherent spin, the interface comprises a quantum memory enabling advanced quantum functionalities. Various experimental implementations of spin–photon interfaces have been studied using, for example, single trapped atoms in cavities, silicon (SiV) or nitrogen (NV) vacancy centers in diamond or self‐assembled quantum dots in gallium arsenide . Here, our main focus will be on implementations where the photon‐emitter coupling efficiency is near unity and highly coherent, which is the limit where spin and photon become deterministically coupled.…”

“…While large photonic cluster states generated by quantum dots may function as quantum memories for two‐way repeaters, the NV systems arguably seem more suited for two‐way repeaters due to the availability of nuclear spin memories. Notably, this also opens up the possibility of performing both entanglement purification and entanglement swapping within the same diamond in a minimum resource setup (see Figure a). Having access to more than a single NV system will, however, allow the repeater to boost its rate through parallel entanglement generation attempts .…”

Optimal design of diamond-air microcavities for quantum networks using an analytical approach

“…Next we determine the diamond thickness-dependency of an NV centre's branching ratio into the ZPL 5 . For this we need to find the linewidth and mode volume: we use the transfer matrix to numerically find the cavity linewidth from the cavity reflectivity as a function of frequency, and we calculate the mode volume using equation (7). The method with which we determine the beam waist w 0 will be later outlined in section 3.…”

“…Nitrogen-vacancy (NV) defect centers in diamond can be used as building blocks for such networks, with a coherent spin-photon interface that enables the generation of heralded distant entanglement [2,3]. The long-lived electron spin and nearby nuclear spins provide quantum memories that are crucial for extending entanglement to multiple nodes and longer distances [4][5][6][7][8]. However, to fully exploit the NV centre as a quantum network building block requires increasing the entanglement success probability.…”

Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels

“…To address this problem, quantum entanglement distillation (QED) algorithms [19][20][21][22][23][24][25][26][27][28][29] have been proposed to generate highly entangled shared qubit pairs from many contaminated ones via local operations and classical communication (LOCC). Since high-quality entanglement is the keystone in many important applications of quantum computation and quantum information, QED has become an essential building block for the development of quantum networks [30][31][32].…”