Abstract
We present a quantum-enhanced atomic clock protocol based on groups of sequentially larger Greenberger-Horne-Zeilinger (GHZ) states, that achieves the best clock stability allowed by quantum theory up to a logarithmic correction. The simultaneous interrogation of the laser phase with such a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the Ramsey interrogation time beyond the laser noise limit. We compare the new protocol with state of the art interrogation schemes, and show that entanglement allow a significant quantum gain in the stability for short averaging time.