More than 50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in 'loopholes'. Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification.

Quantum entanglement between spatially separated objects is one of the most intriguing phenomena in physics. The outcomes of independent measurements on entangled objects show correlations that cannot be explained by classical physics. Besides being of fundamental interest, entanglement is a unique resource for quantum information processing and communication. Entangled qubits can be used to establish private information or implement quantum logical gates [1,2]. Such capabilities are particularly useful when the entangled qubits are spatially separated [3][4][5], opening the opportunity to create highly connected quantum networks [6] or extend quantum cryptography to long distances [7,8]. Here we present a key experiment towards the realization of long-distance quantum networks with solid-state quantum registers. We have entangled two electron spin qubits in diamond that are separated by a three-meter distance. We establish this entanglement using a robust protocol based on local creation of spin-photon entanglement and a subsequent joint measurement of the photons. Detection of the photons heralds the projection of the spin qubits onto an entangled state. We verify the resulting non-local quantum correlations by performing single-shot readout [9] on the qubits in different bases. The long-distance entanglement reported here can be combined with recently achieved initialization, readout and entanglement operations [9-13] on local long-lived nuclear spin registers, enabling deterministic long-distance teleportation, quantum repeaters and extended quantum networks.A quantum network can be constructed by using entanglement to connect local processing nodes, each containing a register of well-controlled and long-lived qubits [6]. Solids are an attractive platform for such registers, as the use of nanofabrication and material design may enable well-controlled and scalable qubit systems [14]. The potential impact of quantum networks on science and technology has recently spurred research efforts towards generating entangled states of distant solid-state qubits [15][16][17][18][19][20][21].A prime candidate for a solid-state quantum register is the nitrogen-vacancy (NV) defect centre in diamond. The NV centre combines a long-lived electronic spin (S=1) with a robust optical interface, enabling measurement and high-fidelity control of the spin qubit [15,[22][23][24]. Furthermore, the NV electron spin can be used to access and manipulate nearby nuclear spins [9-13], thereby forming a multi-qubit register. To use such registers in a quantum network requires a mechanism to coherently connect remote NV centres.Here we demonstrate the generation of entanglement between NV centre spin qubits in distant setups. We achieve this breakthrough by combining recently established spin initialization and single-shot readout techniques [9] with efficient resonant optical detection and feedback-based control over the optical transitions, all in a single experiment and executed with high fidelity. These results put solid-state qubits on ...

Initialization and read-out of coupled quantum systems are essential ingredients for the implementation of quantum algorithms. Single-shot read-out of the state of a multi-quantum-bit (multi-qubit) register would allow direct investigation of quantum correlations (entanglement), and would give access to further key resources such as quantum error correction and deterministic quantum teleportation. Although spins in solids are attractive candidates for scalable quantum information processing, their single-shot detection has been achieved only for isolated qubits. Here we demonstrate the preparation and measurement of a multi-spin quantum register in a low-temperature solid-state system by implementing resonant optical excitation techniques originally developed in atomic physics. We achieve high-fidelity read-out of the electronic spin associated with a single nitrogen-vacancy centre in diamond, and use this read-out to project up to three nearby nuclear spin qubits onto a well-defined state. Conversely, we can distinguish the state of the nuclear spins in a single shot by mapping it onto, and subsequently measuring, the electronic spin. Finally, we show compatibility with qubit control: we demonstrate initialization, coherent manipulation and single-shot read-out in a single experiment on a two-qubit register, using techniques suitable for extension to larger registers. These results pave the way for a test of Bell's inequalities on solid-state spins and the implementation of measurement-based quantum information protocols.

Realizing robust quantum information transfer between long-lived qubit registers is a key challenge for quantum information science and technology. Here we demonstrate unconditional teleportation of arbitrary quantum states between diamond spin qubits separated by 3 meters. We prepare the teleporter through photon-mediated heralded entanglement between two distant electron spins and subsequently encode the source qubit in a single nuclear spin. By realizing a fully deterministic Bell-state measurement combined with real-time feed-forward we achieve teleportation in each attempt while obtaining an average state fidelity exceeding the classical limit. These results establish diamond spin qubits as a prime candidate for the realization of quantum networks for quantum communication and network-based quantum computing.The reliable transmission of quantum states between remote locations is a major open challenge in quantum science today. Quantum state transfer between nodes containing long-lived qubits [1][2][3] can extend quantum key distribution to long distances [4], enable blind quantum computing in the cloud [5] and serve as a critical primitive for a future quantum network [6]. When provided with a single copy of an unknown quantum state, directly sending the state in a carrier such as a photon is unreliable due to inevitable losses. Creating and sending several copies of the state to counteract such transmission losses is impossible by the no-cloning theorem [7]. Nevertheless, quantum information can be faithfully transmitted over arbitrary distances through quantum teleportation provided the network parties (named "Alice" and "Bob") have previously established a shared entangled state and can communicate classically [8][9][10][11].The teleportation protocol is sketched in Fig. 1A. At the start, Alice is in possession of the state to be teleported (qubit 1) which is most generally given by |ψ = α|0 + β|1 . Alice and Bob each have one qubit of an entangled pair (qubits 2 and 3) in the joint state |ΨThe combined state of all three qubits can be rewritten aswhere |Φ ± = (|00 ± |11 )/ √ 2 and |Ψ ± = (|01 ± |10 )/ √ 2 are the four Bell states. To teleport the quantum state Alice performs a joint measurement on her * Present address: Department of Applied Physics, Yale University, New Haven, CT 06511, USA † r.hanson@tudelft.nl qubits (qubits 1 and 2) in the Bell basis, projecting Bob's qubit into a state that is equal to |ψ up to a unitary operation that depends on the outcome of Alice's measurement. Alice sends the outcome via a classical communication channel to Bob, who can then recover the original state by applying the corresponding local transformation.Because the source qubit state always disappears on Alice's side, it is irrevocably lost whenever the protocol fails. Therefore, to ensure that each qubit state inserted into the teleporter unconditionally re-appears on Bob's side, Alice must be able to distinguish between all four Bell states in a single shot and Bob has to preserve the coherence of the target q...