Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.06606 · Physics Letters A

Enhanced Precision in Entangled Quantum Clocks with Phase Estimation Algorithm

Won-Young Hwang

quant-phgr-qcSubmitted Apr 8, 2026• Announced Apr 9, 2026• 0 citations• Revised Sep 16, 2026 (v2)
v1 · Apr 8, 2026v2 · Sep 16, 2026
arXivHTMLPDF

Abstract

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.

Journal reference
Physics Letters A 597 (2026), 132161
Comments
The feasibility of detecting gravitational waves is discussed

Related papers

Heisenberg-Limited Atom Clocks Based on Entangled Qubits

E. M. Kessler, P. Kómár, Michael Bishof +4 more

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.

arXiv:1310.6043•Physical Review Letters•May 15, 2014•126 citations

Experimental optical phase measurement at the exact Heisenberg limit (Conference Presentation)

Shakib Daryanoosh, Sergei Slussarenko, Howard M. Wiseman +1 more

Optical phase measurement through its application in quantum metrology has pushed the precision limit with which some physical quantities can be measured accurately. At the very fundamental level, the laws of quantum mechanics dictate that the uncertainty in phase estimations scales as 1/N, where N is the number of quantum resources employed in the protocol [1]. This is the well known Heisenberg limit (HL) which is quadratically better than the traditional precision limit known as the standard quantum limit (SQL) with uncertainty asymptotically scaling as 1/sqrt{N} [1]. Several experiments have demonstrated that the SQL can be beaten by using an entangled state as the probe and a specific measurement scheme for ab initio estimation of unknown phases [2,3]. It has also been shown experimentally that even in the absence of the entanglement one can measure an unknown phase with imprecision scaling at the HL [4]. In this work we first present a new protocol able to estimate an optical phase at the Heisenberg limit, and then experimentally explore fundamental and practical issues in generating high-quality novel entangled states, for use in this protocol and beyond. Our aim in this study is to measure an unknown phase in the interval [0,2pi) with uncertainty attaining the exact HL. There is a condition that should be met to address this objective: preparation of an optimal state [5]. This would cover part of the presentation through which we explain how to experimentally realise such an optimal state with the current technological limitations and the feasibility of the scheme. In particular, we generate an entangled 3-photon (2-photon) state of specific superposition of GHZ (Bell) states. Our numerical simulation of the phase measurement gate together with the experimental outcomes show that the created state should have a high fidelity and purity to be able to have the phase uncertainty achieving the exact HL. Therefore, we briefly explain the modelling for experimental imperfections and finally present the results of experimental phase measurements.

•Dec 7, 2016•0 citations

Quantum Entanglement-Based Distributed Time Synchronization

Jincheng Zhang

This paper investigates the feasibility and potential of utilizing quantum entanglement for distributed time synchronization. We propose a novel framework leveraging multi-body quantum entanglement to achieve highly precise and secure time synchronization beyond the limitations imposed by classical physics. The core mechanism involves constructing a distributed network of quantum sensors interconnected through entangled states. By measuring the phase shifts within these entangled states and exploiting the inherent properties of quantum entanglement to mitigate error propagation, we demonstrate the possibility of accurately synchronizing the time of all sensors in the network. This approach offers a fundamentally different paradigm compared to traditional methods reliant on classical communication, providing enhanced security and precision. The research highlights the potential for applications requiring ultra-precise timing, such as fundamental physics experiments, advanced sensor networks, and secure communication protocols. We introduce a theoretical model outlining the synchronization process and discuss key challenges and future research directions. ---

•Aug 28, 2026•0 citations

The elusive Heisenberg limit in quantum-enhanced metrology

Rafał Demkowicz-Dobrzański, Jan Kołodyński, Mădălin Guţǎ

Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss. Quantum metrology employs the properties of quantum states to further enhance the accuracy of some of the most precise measurement schemes to date. Here, a method for estimating the upper bounds to achievable precision in quantum-enhanced metrology protocols in the presence of decoherence is presented.

arXiv:1201.3940•Nature Communications•Sep 18, 2012•773 citations

Increasing Sensing Resolution with Error Correction

G. Arrad, Yuval Vinkler-Aviv, Dorit Aharonov +1 more

The signal to noise ratio of quantum sensing protocols scales with the square root of the coherence time. Thus, increasing this time is a key goal in the field. By utilizing quantum error correction, we present a novel way of prolonging such coherence times beyond the fundamental limits of current techniques. We develop an implementable sensing protocol that incorporates error correction, and discuss the characteristics of these protocols in different noise and measurement scenarios. We examine the use of entangled versue untangled states, and error correction's reach of the Heisenberg limit. The effects of error correction on coherence times are calculated and we show that measurement precision can be enhanced for both one-directional and general noise.

arXiv:1310.3016•Physical Review Letters•Apr 16, 2014•201 citations

Quantum-Enhanced Atomic Clocks for Military PNT and Secure Communications

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.

•Jan 1, 2026•0 citations
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.
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.
Optical phase measurement through its application in quantum metrology has pushed the precision limit with which some physical quantities can be measured accurately. At the very fundamental level, the laws of quantum mechanics dictate that the uncertainty in phase estimations scales as 1/N, where N is the number of quantum resources employed in the protocol [1]. This is the well known Heisenberg limit (HL) which is quadratically better than the traditional precision limit known as the standard quantum limit (SQL) with uncertainty asymptotically scaling as 1/sqrt{N} [1]. Several experiments have demonstrated that the SQL can be beaten by using an entangled state as the probe and a specific measurement scheme for ab initio estimation of unknown phases [2,3]. It has also been shown experimentally that even in the absence of the entanglement one can measure an unknown phase with imprecision scaling at the HL [4]. In this work we first present a new protocol able to estimate an optical phase at the Heisenberg limit, and then experimentally explore fundamental and practical issues in generating high-quality novel entangled states, for use in this protocol and beyond. Our aim in this study is to measure an unknown phase in the interval [0,2pi) with uncertainty attaining the exact HL. There is a condition that should be met to address this objective: preparation of an optimal state [5]. This would cover part of the presentation through which we explain how to experimentally realise such an optimal state with the current technological limitations and the feasibility of the scheme. In particular, we generate an entangled 3-photon (2-photon) state of specific superposition of GHZ (Bell) states. Our numerical simulation of the phase measurement gate together with the experimental outcomes show that the created state should have a high fidelity and purity to be able to have the phase uncertainty achieving the exact HL. Therefore, we briefly explain the modelling for experimental imperfections and finally present the results of experimental phase measurements.
This paper investigates the feasibility and potential of utilizing quantum entanglement for distributed time synchronization. We propose a novel framework leveraging multi-body quantum entanglement to achieve highly precise and secure time synchronization beyond the limitations imposed by classical physics. The core mechanism involves constructing a distributed network of quantum sensors interconnected through entangled states. By measuring the phase shifts within these entangled states and exploiting the inherent properties of quantum entanglement to mitigate error propagation, we demonstrate the possibility of accurately synchronizing the time of all sensors in the network. This approach offers a fundamentally different paradigm compared to traditional methods reliant on classical communication, providing enhanced security and precision. The research highlights the potential for applications requiring ultra-precise timing, such as fundamental physics experiments, advanced sensor networks, and secure communication protocols. We introduce a theoretical model outlining the synchronization process and discuss key challenges and future research directions. ---
Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss. Quantum metrology employs the properties of quantum states to further enhance the accuracy of some of the most precise measurement schemes to date. Here, a method for estimating the upper bounds to achievable precision in quantum-enhanced metrology protocols in the presence of decoherence is presented.
The signal to noise ratio of quantum sensing protocols scales with the square root of the coherence time. Thus, increasing this time is a key goal in the field. By utilizing quantum error correction, we present a novel way of prolonging such coherence times beyond the fundamental limits of current techniques. We develop an implementable sensing protocol that incorporates error correction, and discuss the characteristics of these protocols in different noise and measurement scenarios. We examine the use of entangled versue untangled states, and error correction's reach of the Heisenberg limit. The effects of error correction on coherence times are calculated and we show that measurement precision can be enhanced for both one-directional and general noise.
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.