Enhanced precision in entangled quantum clocks with phase estimation algorithm

Won-Young Hwang

We present an enhanced entangled-quantum-clock protocol that incorporates a quantum phase estimation algorithm to directly estimate proper-time differences as an unknown phase. By employing highly entangled multi-clock states, the achievable uncertainty scales inversely with the total number of quantum clocks, achieving the Heisenberg limit $O(1/N)$ while remaining completely immune to dynamical phase noise. Furthermore, we discuss the feasibility of utilizing this ultra-high precision protocol for gravitational wave detection, highlighting its potential for quantum-enhanced relativistic sensing and fundamental physics tests.

Axel André, Anders Søndberg Sørensen, Mikhail D. Lukin

Li-Zheng Liu, Yu-Zhe Zhang, Zheng-Da Li +8 more

Zuhair Ahmed

Abstract Precise timekeeping is a foundational, often overlooked dependency of both positioning/navigation/timing (PNT) systems and secure communications: satellite navigation requires nanosecond-level clock synchronization to compute position from signal time-of-flight, and time-synchronized cryptographic protocols (including key-exchange window validation and frequency-hopping schemes) depend on clock stability at the transmitting and receiving ends. Current-generation atomic clocks (cesium and rubidium standards) achieve their stability by averaging over many independent, unentangled atoms, a strategy fundamentally limited by the standard quantum limit (SQL), in which timing precision scales with the number of atoms N as N. Quantum-enhanced atomic clocks propose replacing independent-atom ensembles with entangled (GHZ-state) ensembles, whose Heisenberg-limited precision scales instead as N². This study validates the two components of that claim independently: (1) the entanglement-derived precision advantage, via GHZ Ramsey spectroscopy simulated on the PKTron quantum computing framework across probe sizes N = 1, 2, 4, and 6, and cross-checked on IBM Quantum's ibm_fez hardware at N = 4; and (2) accurate recovery of an atomic transition's phase signal, via PKTron's built-in Quantum Phase Estimation (QPE) algorithm, tested against three independent reference phases. Simulation reproduced exact Heisenberg scaling (measured Fisher information of 1.00, 4.00, 16.00, and 36.00 against theoretical N² values of 1, 4, 16, and 36) and exact QPE phase recovery (zero measured error across all three test phases). On real IBM Quantum hardware at N = 4, the zero-drift calibration point returned P(all-zero) = 0.972, and the maximum-sensitivity bias point returned P(all-zero) = 0.500, exactly matching the theoretical prediction. These results constitute a reproducible, multi-method, hardware-validated confirmation of the sensing and phase-extraction primitives that underlie quantum-enhanced atomic clock proposals. This work does not simulate or validate a physical atomic clock, an optical lattice clock, or any oscillator hardware; it validates the underlying discrete-variable sensing and estimation mechanisms only, and should be read accordingly.

Raphael Kaubruegger, Adam M. Kaufman

Quantum entanglement offers powerful opportunities for enhancing measurement sensitivity beyond classical limits, with optical atomic clocks serving as a leading platform for such advances. This chapter introduces the principles of entanglement-enhanced quantum metrology and explores their applications to timekeeping. We review the theoretical framework of quantum phase estimation, comparing frequentist and Bayesian approaches, and discuss paradigmatic entangled states such as spin-squeezed and GHZ states. Particular emphasis is placed on the challenges posed by decoherence, which constrain the practical advantages that can be realized in large-scale devices. The discussion then turns to frequency estimation in atomic clocks, highlighting how experimental constraints shape the translation of abstract quantum limits into real performance gains. Finally, we outline emerging directions of contemporary quantum metrology. Together, these developments underscore the increasingly close interplay between quantum information processing and precision metrology.

Jianing Tan, Zhihao Liu, Hanwu Chen