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arXiv:2602.05337 · Physical Review Letters

Entanglement-enhanced quantum metrology via alternating in-phase and quadrature modulation

Jihao Ma, Jiahao Huang, Chaohong Lee

quant-phphysics.atom-phSubmitted Feb 5, 2026• Announced Feb 6, 2026• 1 citation
arXivHTMLPDF

Abstract

Quantum metrology harnesses quantum entanglement to improve measurement precision beyond standard quantum limit. Although nonlinear interaction is essential for generating entanglement, during signal accumulation, it becomes detrimental and therefore must be suppressed. To address this challenge, we propose an alternating in-phase and quadrature modulation (AIQM) scheme, designed to operate under a fixed nonlinear interaction. During signal accumulation, our time-interleaved approach sequentially applies the in-phase and quadrature driving fields, thereby eliminating the effects of nonlinear interaction on signal accumulation. Our AIQM scheme achieves better metrological performance than conventional schemes, particularly under strong nonlinear interaction and prolonged signal accumulation, with pronounced robustness against parameter variations. By selectively eliminating and utilizing nonlinear interactions via AIQM, our work enables high-precision and high-accuracy entanglement-enhanced sensing without the need for active control of the nonlinear interaction.

Journal reference
Phys. Rev. Lett. 137, 100801 (2026)
DOI
10.1103/djlj-pnlk
Comments
8 pages, 4 figures

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Quantum metrology harnesses quantum entanglement to improve measurement precision beyond standard quantum limit. Although nonlinear interaction is essential for generating entanglement, during signal accumulation, it becomes detrimental and therefore must be suppressed. To address this challenge, we propose an alternating in-phase and quadrature modulation (AIQM) scheme, designed to operate under a fixed nonlinear interaction. During signal accumulation, our time-interleaved approach sequentially applies the in-phase and quadrature driving fields, thereby eliminating the effects of nonlinear interaction on signal accumulation. Our AIQM scheme achieves better metrological performance than conventional schemes, particularly under strong nonlinear interaction and prolonged signal accumulation, with pronounced robustness against parameter variations. By selectively eliminating and utilizing nonlinear interactions via AIQM, our work enables high-precision and high-accuracy entanglement-enhanced sensing without the need for active control of the nonlinear interaction.
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Quantum optimal control (QOC) schemes can be employed to enhance the sensitivity of quantum metrology (QM) protocols undergoing Markovian noise, which can limit their precision to a standard quantum limit (SQL)-like scaling. In this paper, we propose a QOC scheme for QM that leverages entanglement and optimized coupling interactions with an ancillary system to provide enhanced metrological performance under general Markovian dynamics. We perform a comparative analysis of our entanglement-enhanced scheme against the unentangled scheme conventionally employed in QOC-enabled QM for varying evolution times and decoherence levels, revealing that the entanglement-enhanced scheme enables significantly better noise performance, even when a noisy ancilla is employed. We further extend our investigation to time-inhomogeneous noise models, specifically focusing on a noisy frequency estimation scenario within a spin-boson bath, and evaluate the protocol's performance under completely dissipative and dephasing dynamics. Our findings indicate that, in certain situations, schemes employing coherent control of a single particle are severely limited. In such cases, employing the entanglement-enhanced scheme can provide improved performance.
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Abstract Entanglement is one of the key ingredients for enhancing the measurement precision of quantum sensors. Generally, there is a trade-off between state preparation and sensing within a limited coherence time. To fully exploit temporal resources, concurrent entanglement generation and sensing with designed sequence of rotations are proposed. Based on twist-and-turn dynamics, modulated rotations along only one axis may be sufficient to drive the state to the optimal one for tiny estimated parameter. However, when the estimated parameter is not tiny, it may impact the evolved state and hence degrade the final measurement precision. Here, we introduce another modulated rotations along different axis and find out the optimal control sequences by means of machine optimization. The optimal measurement precision bounds become independent on the estimated parameter, which improves the dynamic range of the machine designed sensors. Particularly, by optimizing the interaction strength for different particle number and the time-modulated rotations along two different axes via machine optimization, the Heisenberg-limited precision scaling can be attained. Our work points out a way for designing optimized quantum-enhanced metrology protocols, which is promising for developing practical quantum sensors.
Nonlinear effects are widely utilized in quantum metrology to enhance measurement precision by leveraging complex dynamical behaviors. Here, we propose a quantum scrambling-integrated scheme that optimizes the selection of initial states and parameter encoding by exploiting the nonlinear dynamical trajectories and their geometric properties in phase space. We consider a two-mode Bose-Einstein condensate as a typical example. Within a certain parameter range, using uncorrelated spin coherent states located at saddle points and separatrices enables the measurement precision to reach the Heisenberg scaling. An analytical expression for the quantum Fisher information under long-time evolution is provided, and our analysis further reveals that the enhancement mechanism is governed by the sensitivity of the energy spectrum to parameter variations. Compared to the criticality-enhanced protocol that requires parameters to approach the critical point, our scheme offers a distinct advantage in its applicability over a broader range of parameters. Moreover, this scheme can also be applied to models that include one- and two-axis countertwisting interactions and chaotic dynamics. This Letter offers a new perspective for advancing the application of nonlinear dynamics to enhance the parameter estimation precision in quantum systems.