Abstract

Optical atomic clocks are our most precise tools to measure time and frequency [4] and the properties of dark matter [5,6], to perform geodesy [4,7,8] and to evaluate systematic clock shifts. Measurements on independent systems are limited by the standard quantum limit (SQL); measurements on entangled systems, in contrast, can surpass the SQL to reach the ultimate precision allowed by quantum theory — the so-called Heisenberg limit. While local entangling operations have been used to demonstrate this enhancement at microscopic distances [^9-14], frequency comparisons between remote atomic clocks require rapid high-fidelity entanglement between separate systems that have no intrinsic interactions.

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