A nondestructive Bell-state measurement on two distant atomic qubits

One of the most fascinating aspects of quantum networks is their capability to distribute entanglement as a nonlocal communication resource. In a first step, this requires network-ready devices that can generate and store entangled states. Another crucial step, however, is to develop measurement techniques that allow for entanglement detection. Demonstrations for different platforms suffer from being either not complete, or destructive, or local. Here we demonstrate a complete and nondestructive measurement scheme that always projects any initial state of two spatially separated network nodes onto a maximally entangled state. Each node consists of an atom trapped inside an optical resonator from which two photons are successively reflected. Polarisation measurements on the photons discriminate between the four maximally entangled states. Remarkably, such states are not destroyed by our measurement. In the future, our technique might serve to probe the decay of entanglement and to stabilise it against dephasing via repeated measurements.