Optical atomic clocks are our most precise tools to measure time and frequency1-3. Precision frequency comparisons between clocks in separate locations enable one to probe the space-time variation of fundamental constants4,5 and the properties of dark matter6,7, to perform geodesy8-10 and to evaluate systematic clock shifts. Measurements on independent systems are limited by the standard quantum limit; measurements on entangled systems can surpass the standard quantum limit to reach the ultimate precision allowed by quantum theory-the Heisenberg limit. Although local entangling operations have demonstrated this enhancement at microscopic distances11-16, comparisons between remote atomic clocks require the rapid generation of high-fidelity entanglement between systems that have no intrinsic interactions. Here we report the use of a photonic link17,18 to entangle two 88Sr+ ions separated by a macroscopic distance19 (approximately 2 m) to demonstrate an elementary quantum network of entangled optical clocks. For frequency comparisons between the ions, we find that entanglement reduces the measurement uncertainty by nearly [Formula: see text], the value predicted for the Heisenberg limit. Today's optical clocks are typically limited by dephasing of the probe laser20; in this regime, we find that entanglement yields a factor of 2 reduction in the measurement uncertainty compared with conventional correlation spectroscopy techniques20-22. We demonstrate this enhancement for the measurement of a frequency shift applied to one of the clocks. This two-node network could be extended to additional nodes23, to other species of trapped particles or-through local operations-to larger entangled systems.
© 2022. The Author(s), under exclusive licence to Springer Nature Limited.