Quantum computing and networking with trapped ions; or - Two things to do with two qubits two metres apart

I will describe two recent experiments performed using an elementary two-node quantum network at Oxford, which links two independent ion traps, separated by 2 metres, via a single-photon optical fibre interface. Both experiments rely on the ability to generate high-fidelity (>90%) entanglement between trapped-ion qubits, one stored in each trap, at high speed (up to 200 entanglement events per second). In the first experiment [Nadlinger et al., arXiv 2021] we present a realization of a complete quantum key distribution (QKD) protocol immune to the vulnerabilities of the physical devices used in the implementation. In this "device-independent" QKD protocol, we can put a limit on the amount of information accessible to an eavesdropping adversary by using Bell's Theorem, as first proposed 30 years ago by Ekert [Phys.Rev.Lett. 1991]. The second experiment [Nichol et al., arXiv 2021] uses the remote entanglement as a resource to enhance the precision attainable in comparing the frequency of a narrow optical transition in each ion, as is required for accurate comparisons of optical clocks, with applications to probing the space-time variation of fundamental constants, searching for exotic particles, or geodesy. We surpass the "standard quantum limit" which applies to independent systems, and approach the so-called Heisenberg limit, the ultimate measurement precision attainable for entangled particles. This halves the averaging time needed to reach a given precision; if the precision is limited by dephasing of the spectroscopy laser, as is typically the case for today's optical clocks, then the use of entanglement gives a further factor of 2 improvement. Prospects for future experiments, with application to quantum computing, will be discussed.