Large-scale quantum networks promise to enable secure communication, distributed quantum computing, enhanced sensing and fundamental tests of quantum mechanics through the distribution of entanglement across nodes [1] [2] [3] [4] [5] [6] [7] . Moving beyond current two-node networks [8] [9] [10] [11] [12] [13] requires the rate of entanglement generation between nodes to exceed their decoherence rates. Beyond this critical threshold, intrinsically probabilistic entangling protocols can be subsumed into a powerful building block that deterministically provides remote entangled links at pre-specified times. Here we surpass this threshold using diamond spin qubit nodes separated by 2 metres. We realise a fully heralded single-photon entanglement protocol that achieves entangling rates up to 39 Hz, three orders of magnitude higher than previously demonstrated two-photon protocols on this platform [14] . At the same time, we suppress the decoherence rate of remote entangled states to 5 Hz by dynamical decoupling. By combining these results with efficient charge-state control and mitigation of spectral diffusion, we are able to deterministically deliver a fresh remote state with average entanglement fidelity exceeding 0.5 at every clock cycle of ∼100 ms without any pre-or post-selection. These results demonstrate a key building block for extended quantum networks and open the door to entanglement distribution across multiple remote nodes. The power of future quantum networks will derive from entanglement that is shared between the network nodes. Two critical parameters for the performance of such networks are the entanglement generation rate r ent between nodes and the entangled-state decoherence rate r dec . Their ratio, that we term the quantum link efficiency η link = r ent /r dec [8, 15] , quantifies how effectively entangled states can be preserved over the timescales necessary to generate them. Alternatively, from a complementary perspective, the link efficiency determines the average number of entangled states that can be created within one entangled state lifetime. Achieving a link efficiency of unity therefore represents a critical threshold beyond which entanglement can be generated faster than it is lost. Exceeding this threshold is central to allowing multiple entangled links to be created and maintained simultaneously, as required for the distribution of manybody quantum states across a network [6, 15] . Consider an elementary entanglement delivery protocol that delivers states at pre-determined times. This can be achieved by making multiple attempts to generate entanglement, and then protecting successfully generated entangled states from decoherence until the required delivery time (Fig. 1a, steps 1, 2 & 3) . If we try to generate entanglement for a period t ent , the cumulative probability of success will be p succ = 1 − e −renttent . For a given p succ , the average fidelity F succ of the successfully generated states is solely determined by the quantum link efficiency η link (Supplementary Information (SI) section I). We plot F succ versus p succ for several values of η link in Fig 1b. This protocol allows entangled states to be delivered at specified times, but with a finite probability of success. By delivering an unentangled state (state fidelity F unent ≤ 1 2 ) in cycles in which all entanglement generation attempts failed, the protocol can be cast into a fully deterministic black-box (Fig 1a, step 4) . The states output from such a black-box will have a fidelity with a Bell state of The maximum achievable fidelity F max det of this deterministic state delivery protocol, found by optimising p succ , is also only determined by the quantum link efficiency η link . For F unent = 1 4 (fully mixed state), we find (see Fig 1c) : Beyond the threshold η link 0.83, there exists a combination of p succ and F succ high enough to compensate for cycles in which entanglement is not heralded, allowing for the deterministic delivery of states that are onaverage entangled (F max det ≥ 1 2 ). Demonstrating deterministic entanglement delivery therefore presents a critical benchmark of a network's performance, certifying that the network quantum link efficiency is of order unity or higher. Furthermore, the ability to specify in advance the time at which entangled states are delivered may assist in designing multi-step quantum information tasks such as entanglement routing [16, 17] . To date, this threshold has remained out of reach for solid-state quantum networks. Quantum dots have demonstrated kHz entanglement rates r ent , but tens of MHz decoherence rates r dec limit their achieved quantum link efficiencies to η link ∼ 10 −4 [18, 19] . Nitrogen vacancy (NV) centres, point-defects in diamond with a long-lived electron spin and bright optical transitions, have demonstrated entanglement rates r ent of tens of mHz [10, 14] and, in separate experiments, decoherence rates r dec of order 1 Hz [20] , which would together give η link ∼ 10 −2 . arXiv:1712.07567v2 [quant-ph]
In REF , the authors defined a method for deterministic delivery of quantum entanglement on a quantum network.
Deterministic delivery of remote entanglement on a quantum network
Nature 558, pages 268-273 (2018)
Computer Science Physics Medicine