N. Sangouard

We present an architecture for remotely connecting cavity-coupled trapped ions via a quantum repeater based on rare-earth-doped crystals. The main challenge for its realization lies in interfacing these two physical platforms, which produce photons with a typical temporal mismatch of one or two orders of magnitude. To address this, we propose an efficient protocol that enables custom temporal reshaping of single-photon pulses whilst preserving purity. Our approach is to modify a commonly used memory protocol, called atomic frequency comb, for systems exhibiting inhomogeneous broadening like rare-earth-doped crystals. Our results offer a viable solution for uniting quantum processing nodes with a quantum repeater backbone.

We report on an elementary quantum network of two atomic ions separated by 230 m. The ions are trapped in different buildings and connected with 520(2) m of optical fiber. At each network node, the electronic state of an ion is entangled with the polarization state of a single cavity photon; subsequent to interference of the photons at a beamsplitter, photon detection heralds entanglement between the two ions. Fidelities of up to $(88.2+2.3-6.0)\%$ are achieved with respect to a maximally entangled Bell state, with a success probability of $4 \times 10^{-5}$. We analyze the routes to improve these metrics, paving the way for long-distance networks of entangled quantum processors.

Cryptographic key exchange protocols traditionally rely on computational conjectures such as the hardness of prime factorisation to provide security against eavesdropping attacks. Remarkably, quantum key distribution protocols like the one proposed by Bennett and Brassard provide information-theoretic security against such attacks, a much stronger form of security unreachable by classical means. However, quantum protocols realised so far are subject to a new class of attacks exploiting implementation defects in the physical devices involved, as demonstrated in numerous ingenious experiments. Following the pioneering work of Ekert proposing the use of entanglement to bound an adversary's information from Bell's theorem, we present here the experimental realisation of a complete quantum key distribution protocol immune to these vulnerabilities. We achieve this by combining theoretical developments on finite-statistics analysis, error correction, and privacy amplification, with an event-ready scheme enabling the rapid generation of high-fidelity entanglement between two trapped-ion qubits connected by an optical fibre link. The secrecy of our key is guaranteed device-independently: it is based on the validity of quantum theory, and certified by measurement statistics observed during the experiment. Our result shows that provably secure cryptography with real-world devices is possible, and paves the way for further quantum information applications based on the device-independence principle.

Trapped atomic ions embedded in optical cavities are a promising platform to enable long-distance quantum networks and their most far-reaching applications. Here we achieve and analyze photon indistinguishability in a telecom-converted ion-cavity system. First, two-photon interference of cavity photons at their ion-resonant wavelength is observed and found to reach the limits set by spontaneous emission. Second, this limit is shown to be preserved after a two-step frequency conversion replicating a distributed scenario, in which the cavity photons are converted to the telecom C band and then back to the original wavelength. The achieved interference visibility and photon efficiency would allow for the distribution and practical verification of entanglement between ion-qubit registers separated by several tens of kilometers.

Quantum repeaters provide an efficient solution to distribute Bell pairs over arbitrarily long distances. While scalable architectures are demanding regarding the number of qubits that need to be controlled, here we present a quantum repeater scheme aiming to extend the range of present day quantum communications that could be implemented in the near future with trapped ions in cavities. We focus on an architecture where ion-photon entangled states are created locally and subsequently processed with linear optics to create elementary links of ion-ion entangled states. These links are then used to distribute entangled pairs over long distances using successive entanglement swapping operations performed deterministically using ion-ion gates. We show how this architecture can be implemented while encoding the qubits in a decoherence free subspace to protect them against collective dephasing. This results in a protocol that can be used to violate a Bell inequality over distances of about 800 km assuming state of the art parameters. We discuss how this could be improved to several thousand kilometers in future setups.

The endeavour to develop quantum networks gave rise to a rapidly developing field with far reaching applications such as secure communication and the realisation of distributed computing tasks. This ultimately calls for the creation of flexible multi-user structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multi-user applications. To address this challenge, we propose a 2D quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multi-qubit entanglement structures at growing scale, where variants of entanglement swapping and multi-party entanglement purification are combined to create high fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.