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Quantum-Enhanced Atomic Clocks for Military PNT and Secure Communications

Zuhair Ahmed

Published Jan 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-10838339/v1

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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.
Abstract Quantum-enhanced positioning, navigation, and timing (Quantum PNT) has been proposed as a partial mitigation for Global Navigation Satellite System (GNSS) denial, jamming, and spoofing in contested operational environments. The physical mechanism underlying proposed quantum inertial sensors — cold-atom accelerometers and gyroscopes — is quantum-enhanced phase estimation using entangled Greenberger-Horne-Zeilinger (GHZ) probe states, which in principle allows measurement precision to scale with probe size N as the Heisenberg limit (N² Fisher information) rather than the classical standard quantum limit (N). This study isolates that sensing primitive, implements it as a qubit circuit, and validates it in two stages: (1) a noiseless statevector simulation using the PKTron quantum computing framework across probe sizes N = 1, 2, 4, and 6, and (2) a single-point hardware validation of the N = 4 case on IBM Quantum's ibm_fez superconducting processor via Qiskit Runtime. The 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). On real hardware, the circuit's zero-signal calibration point returned P(all-zero) = 0.981, and its maximum-sensitivity bias point returned P(all-zero) = 0.477 against a theoretical value of 0.500, a deviation of approximately 2.3 percentage points attributable to gate and readout noise. These results constitute a reproducible, hardware-validated demonstration of the quantum sensing primitive that underlies Quantum PNT proposals. This work explicitly does not constitute a demonstration, prototype, or validation of an operational navigation system; it validates the elementary phase-sensing building block only, under idealized and near-idealized conditions, and is offered as a ready-to-run circuit reference for groups with access to atomic or trapped-ion sensing hardware.
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. Importantly the protocol is designed to work under realistic conditions where the drift of the phase of the laser interrogating the atoms is the main source of decoherence. The simultaneous interrogation of the laser phase with a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the coherent interrogation time beyond the laser noise limit. We compare and merge the new protocol with existing state of the art interrogation schemes, and identify the precise conditions under which entanglement provides an advantage for clock stabilization: it allows a significant gain in the stability for short averaging time.
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.
Optical atomic clocks with unrivaled precision and accuracy have advanced the frontier of precision measurement science and opened new avenues for exploring fundamental physics. A fundamental limitation on clock precision is the standard quantum limit (SQL), which stems from the uncorrelated projection noise of each atom. State-of-the-art optical lattice clocks interrogate large ensembles to minimize the SQL, but density-dependent frequency shifts pose challenges to scaling the atom number. The SQL can be surpassed, however, by leveraging entanglement, though it remains an open problem to achieve quantum advantage from spin squeezing at state-of-the-art stability levels. Here, we demonstrate clock performance beyond the SQL, achieving a fractional frequency precision of 1.1×10^{-18} for a single spin-squeezed clock. With cavity-based quantum nondemolition measurements, we prepare two spin-squeezed ensembles of ∼30 000 strontium atoms confined in a two-dimensional optical lattice. A synchronous clock comparison with an interrogation time of 61 ms achieves a metrological improvement of 2.0(2) dB beyond the SQL, after correcting for state preparation and measurement errors. These results establish the most precise entanglement-enhanced clock to date and offer a powerful platform for exploring the interplay of gravity and quantum entanglement.
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)O(1/N)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.
Accurate timekeeping is essential for scientific and technological advancements, particularly in areas of communication, networking, navigation, and high precision measurements. While many methods of time resolution are already established using classical resources, they fail to combine high precision outcomes with large-scale implementations. Additionally, numerous quantum networking architectures using satellite-assisted methods have demonstrated quantum communication on scales exceeding ground-based methods. For these reasons, we propose the use of a time synchronization method by which pairs of highly time-correlated photons are exchanged between clocks on satellites and clocks on Earth, al- lowing users to reconstruct the time offsets between their clocks. This is known as Quantum Clock Synchronization (QCS). We analyze global time synchronization, via numerical simulation, using a network of satellites equipped with quantum resources, such as entangled photon sources (SPDC) and single photon detectors. We find that for satellites in low-earth orbits, a configuration of 50 evenly-space satellites provides constant visibility and sub-nanosecond time synchronization to any location on Earth. Due to practical constraints, clocks available for use on satellites are often of lesser quality than those available for ground use. However, by allowing the satellites in our network to synchronize among themselves, we overcome this limitation, forming a highly precise “master clock” capable of global, high precision time synchronization. We then examine the amount of quantum security provided by polarization-entangled photon sources as a potential way to protect an experimental implementation of QCS from attacks such as signal spoofing. To do this, we identify regions on Earth where Bell violations between exchanged entangled photons can ensure quantum security at various confidence vii levels. Combined with similar insights gained from determining the network scale of our QCS protocol at the single-link level, we demonstrate the potential for highly precise, global, and potentially quantum-secure clock synchronization. Finally, we modify our QCS protocol to support frequency, or tick-rate, offsets in addition to constant time offsets. We motivate this by presenting some relativistic effects that can introduce frequency differences between clocks in space and on Earth. Provided that relative velocities between clocks are corrected for, we identify constant and variable clock defects through numerical simulations.