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

Advanced Quantum Technologies

Squeezing Enhanced Two Phase Estimation With N Particle W States

Huan Zhang, Guofu Yin, Ying Xia, Bing He, Xiuxing Zhang, Shoukang Chang, Wei Ye

Published Aug 30, 2026• 0 citations
Publisher

Abstract

ABSTRACT Simultaneous estimation of two optical phases in a three‐mode interferometer assisted by optical parametric amplification (OPA) is investigated. The normally ordered characteristic function formalism is employed to derive analytical expressions for all photon number moments of the output state, allowing explicit evaluation of the quantum Fisher information matrix for multiparameter estimation. In the lossless regime, uniformly applied OPA significantly improves the attainable precision compared with an unamplified interferometer. As the OPA gain increases, the quantum Cramér–Rao bound gradually approaches Heisenberg scaling, resulting from the combined effects of increased photon resources and squeezing‐induced modification of photon number statistics. Examination of second‐order correlation functions indicates that this enhancement originates from amplified intra mode photon number correlations, rather than inter mode correlations. The analysis is extended to lossy interferometers using a purification‐based variational approach. Although photon loss reduces the achievable precision, the OPA assisted scheme preserves a clear advantage in the moderate loss regime, demonstrating robustness against dissipation. These findings clarify the physical origin of OPA enhanced performance and provide guidance for optimizing multiparameter phase estimation protocols in realistic noisy settings.

DOI
10.1002/qute.70426

Related papers

Squeezing-Enhanced Two-Phase Estimation with N-Particle W-type States

Huan Zhang, Guofu Yin, Ying Xia +3 more

We investigate the simultaneous estimation of two optical phases in a three-mode interferometer assisted by optical parametric amplification (OPA). By employing the normally ordered characteristic-function formalism, we analytically obtain all photon-number moments of the output quantum state, enabling an explicit evaluation of the quantum Fisher information matrix for multiparameter phase estimation. In the lossless scenario, we show that uniformly applied OPA significantly enhances the attainable precision beyond that of an unamplified interferometer. By analyzing the second-order correlation functions, we demonstrate that this enhancement originates from the amplification of intra-mode photon-number correlations, rather than from inter-mode correlations. We further extend our analysis to realistic interferometers with photon loss using a purification-based variational approach. Although loss degrades the achievable precision, the OPA-assisted scheme retains a clear advantage for moderate loss, indicating a degree of robustness against dissipation. Our results clarify the physical mechanism underlying OPA-enhanced multiparameter quantum metrology and provide guidelines for optimizing phase estimation protocols in realistic noisy environments.

quant-pharXiv:2601.05595•Jan 12, 2026•0 citations

Quantum-enhanced Phase Estimation in Optical Interferometry

Jaspreet Sahota

Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.

•Nov 1, 2017•0 citations

Two‐Parameter Estimation Via Photon Subtraction Operation Within a Feedback‐Assisted Interferometer

Qingqian Kang, Zekun Zhao, Qisi Zhou +5 more

Abstract In this paper, the effect of multi‐photon subtraction operations in a feedback‐assisted interferometer can enhance measurement precision for single‐parameter and two‐parameter estimation is analyzed under both ideal and photon‐loss conditions. The effects of the feedback strength , the optical parametric amplifier's gain , the coherent state amplitude , and the order of multi‐photon subtraction on system performance are examined. It is demonstrated that an optimal feedback strength exists in both conditions. Selecting a suitable can significantly boost the system's robustness to photon loss, and markedly improve measurement precision. And the photon subtraction operations within a feedback‐assisted interferometer can further enhance measurement precision effectively. Additionally, it is found that increasing intramode correlations while decreasing intermode correlations can improve estimation accuracy. This work investigates a new method through the synergistic integration of feedback topology and non‐Gaussian operations into a multiparameter estimation system, along with their systematic study under both ideal and loss conditions. The findings may contribute to improving quantum‐enhanced measurements and hold promise for high‐precision quantum sensing research.

arXiv:2506.05756•Advanced Quantum Technologies•Oct 6, 2025•1 citation

Intramode-correlation–enhanced simultaneous multiparameter-estimation precision

Shoukang Chang, Wei Ye, Xuan Rao +8 more

The multiparameter estimation in quantum metrology is significant for a large number of applications for quantum information tasks. Nevertheless, how mode correlations affect the multiparameter-estimation precision with and without photon-loss cases remains ambiguous. For this reason, here, we present the relationship between the quantum Cram\'er-Rao bound and the mode correlations in the framework of the simultaneous two-phase estimation for a three-mode Mach-Zehnder interferometer induced by the tritter which is composed of three cascaded beam splitters and phase shifters. By choosing different input resources, including a two-mode squeezed vacuum state $\ensuremath{\bigotimes}$ a coherent state (scheme I) and a twin squeezed vacuum state $\ensuremath{\bigotimes}$ a coherent state (scheme II), the results show that compared with scheme II, scheme I shows a better estimation performance even in the presence of photon losses. The reason may be that the intramode correlation of the probe state for scheme I is stronger than that for scheme II, while the intermode correlation of the probe state for the former is weaker than that for the latter. This allow us to open vital perspectives on the essence of enhanced multiparameter-estimation precision.

Physical Review A•Dec 8, 2022•9 citations

Squeezed light and coherent feedback enhanced multiparameter quantum estimation in a double-cavity optomechanics: steady and dynamical states

Hamza Harraf, Mohamed Amazioug, Amjad Sohail +2 more

Multiparameter quantum estimation in open optomechanical systems is fundamentally constrained by dissipation, thermal fluctuations, and measurement incompatibility. In this work, we investigate a coupled cavity optomechanical platform in which two mechanical modes interact with driven optical cavities, two mode squeezed vacuum, intracavity degenerate parametric amplification, and coherent optical feedback. Using the continuous variable Gaussian state formalism, we derive the linearized quantum Langevin dynamics and steady state covariance matrix and evaluate the quantum Fisher information matrices associated with simultaneous estimation of the optomechanical coupling strength and cavity dissipation rate. We characterize the precision bounds using the symmetric and right logarithmic derivative formalisms and employ $\mathcal{B}_{\rm MI}=\max\{\mathcal{B}_S,\mathcal{B}_R\}$ as a comparative figure of merit within the SLD/RLD framework. We find that parametric amplification can substantially reduce the most informative bound, $\mathcal{B}_{\rm MI}$, thereby enhancing multiparameter estimation precision over a broad range of operating conditions. Coherent feedback can further reduce $\mathcal{B}_{\rm MI}$ and improve the estimation precision, particularly in the strong feedback regime. Moreover, the simultaneous presence of coherent feedback, parametric amplification, and squeezed light injection provides a combined mechanism for controlling quantum fluctuations and parameter dependent correlations, leading to enhanced and more robust multiparameter estimation. We further analyze the dynamical and steady state regimes to identify the parameter regions in which these quantum resources provide the largest metrological gain. Our results establish coupled cavity optomechanics as a flexible platform for quantum-noise engineering in multiparameter sensing.

quant-pharXiv:2609.05402•Sep 7, 2026•0 citations

Bounds to precision for quantum interferometry with Gaussian states and operations

Carlo Sparaciari, Stefano Olivares, Matteo G. A. Paris

We address high-precision measurements by active and passive interferometric schemes based on Gaussian states and operations. In particular, we look for the best states to be injected into their ports according to the quantum Cramer–Rao bound, i.e., maximizing the quantum Fisher information over all the involved parameters, given a constraint on the overall mean number of photons entering into the interferometer. We found that for passive interferometers involving only beam splitters, the optimal input leading to Heisenberg scaling is a pair of identical squeezed-coherent states with at most one-third of the total energy employed in squeezing. For active interferometers involving optical amplifiers, input coherent signals are enough to achieve Heisenberg scaling, given an optimal value of the amplification gain. For passive schemes our results clarify the role of squeezing in improving both the reference phase and the signal phase of an interferometer.

Journal of the Optical Society of America B•Jun 5, 2015•60 citations
ABSTRACT Simultaneous estimation of two optical phases in a three‐mode interferometer assisted by optical parametric amplification (OPA) is investigated. The normally ordered characteristic function formalism is employed to derive analytical expressions for all photon number moments of the output state, allowing explicit evaluation of the quantum Fisher information matrix for multiparameter estimation. In the lossless regime, uniformly applied OPA significantly improves the attainable precision compared with an unamplified interferometer. As the OPA gain increases, the quantum Cramér–Rao bound gradually approaches Heisenberg scaling, resulting from the combined effects of increased photon resources and squeezing‐induced modification of photon number statistics. Examination of second‐order correlation functions indicates that this enhancement originates from amplified intra mode photon number correlations, rather than inter mode correlations. The analysis is extended to lossy interferometers using a purification‐based variational approach. Although photon loss reduces the achievable precision, the OPA assisted scheme preserves a clear advantage in the moderate loss regime, demonstrating robustness against dissipation. These findings clarify the physical origin of OPA enhanced performance and provide guidance for optimizing multiparameter phase estimation protocols in realistic noisy settings.
We investigate the simultaneous estimation of two optical phases in a three-mode interferometer assisted by optical parametric amplification (OPA). By employing the normally ordered characteristic-function formalism, we analytically obtain all photon-number moments of the output quantum state, enabling an explicit evaluation of the quantum Fisher information matrix for multiparameter phase estimation. In the lossless scenario, we show that uniformly applied OPA significantly enhances the attainable precision beyond that of an unamplified interferometer. By analyzing the second-order correlation functions, we demonstrate that this enhancement originates from the amplification of intra-mode photon-number correlations, rather than from inter-mode correlations. We further extend our analysis to realistic interferometers with photon loss using a purification-based variational approach. Although loss degrades the achievable precision, the OPA-assisted scheme retains a clear advantage for moderate loss, indicating a degree of robustness against dissipation. Our results clarify the physical mechanism underlying OPA-enhanced multiparameter quantum metrology and provide guidelines for optimizing phase estimation protocols in realistic noisy environments.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.
Abstract In this paper, the effect of multi‐photon subtraction operations in a feedback‐assisted interferometer can enhance measurement precision for single‐parameter and two‐parameter estimation is analyzed under both ideal and photon‐loss conditions. The effects of the feedback strength , the optical parametric amplifier's gain , the coherent state amplitude , and the order of multi‐photon subtraction on system performance are examined. It is demonstrated that an optimal feedback strength exists in both conditions. Selecting a suitable can significantly boost the system's robustness to photon loss, and markedly improve measurement precision. And the photon subtraction operations within a feedback‐assisted interferometer can further enhance measurement precision effectively. Additionally, it is found that increasing intramode correlations while decreasing intermode correlations can improve estimation accuracy. This work investigates a new method through the synergistic integration of feedback topology and non‐Gaussian operations into a multiparameter estimation system, along with their systematic study under both ideal and loss conditions. The findings may contribute to improving quantum‐enhanced measurements and hold promise for high‐precision quantum sensing research.
The multiparameter estimation in quantum metrology is significant for a large number of applications for quantum information tasks. Nevertheless, how mode correlations affect the multiparameter-estimation precision with and without photon-loss cases remains ambiguous. For this reason, here, we present the relationship between the quantum Cram\'er-Rao bound and the mode correlations in the framework of the simultaneous two-phase estimation for a three-mode Mach-Zehnder interferometer induced by the tritter which is composed of three cascaded beam splitters and phase shifters. By choosing different input resources, including a two-mode squeezed vacuum state $\ensuremath{\bigotimes}$ a coherent state (scheme I) and a twin squeezed vacuum state $\ensuremath{\bigotimes}$ a coherent state (scheme II), the results show that compared with scheme II, scheme I shows a better estimation performance even in the presence of photon losses. The reason may be that the intramode correlation of the probe state for scheme I is stronger than that for scheme II, while the intermode correlation of the probe state for the former is weaker than that for the latter. This allow us to open vital perspectives on the essence of enhanced multiparameter-estimation precision.
Multiparameter quantum estimation in open optomechanical systems is fundamentally constrained by dissipation, thermal fluctuations, and measurement incompatibility. In this work, we investigate a coupled cavity optomechanical platform in which two mechanical modes interact with driven optical cavities, two mode squeezed vacuum, intracavity degenerate parametric amplification, and coherent optical feedback. Using the continuous variable Gaussian state formalism, we derive the linearized quantum Langevin dynamics and steady state covariance matrix and evaluate the quantum Fisher information matrices associated with simultaneous estimation of the optomechanical coupling strength and cavity dissipation rate. We characterize the precision bounds using the symmetric and right logarithmic derivative formalisms and employ BMI=max⁡{BS,BR}\mathcal{B}_{\rm MI}=\max\{\mathcal{B}_S,\mathcal{B}_R\}BMI​=max{BS​,BR​} as a comparative figure of merit within the SLD/RLD framework. We find that parametric amplification can substantially reduce the most informative bound, BMI\mathcal{B}_{\rm MI}BMI​, thereby enhancing multiparameter estimation precision over a broad range of operating conditions. Coherent feedback can further reduce BMI\mathcal{B}_{\rm MI}BMI​ and improve the estimation precision, particularly in the strong feedback regime. Moreover, the simultaneous presence of coherent feedback, parametric amplification, and squeezed light injection provides a combined mechanism for controlling quantum fluctuations and parameter dependent correlations, leading to enhanced and more robust multiparameter estimation. We further analyze the dynamical and steady state regimes to identify the parameter regions in which these quantum resources provide the largest metrological gain. Our results establish coupled cavity optomechanics as a flexible platform for quantum-noise engineering in multiparameter sensing.
We address high-precision measurements by active and passive interferometric schemes based on Gaussian states and operations. In particular, we look for the best states to be injected into their ports according to the quantum Cramer–Rao bound, i.e., maximizing the quantum Fisher information over all the involved parameters, given a constraint on the overall mean number of photons entering into the interferometer. We found that for passive interferometers involving only beam splitters, the optimal input leading to Heisenberg scaling is a pair of identical squeezed-coherent states with at most one-third of the total energy employed in squeezing. For active interferometers involving optical amplifiers, input coherent signals are enough to achieve Heisenberg scaling, given an optimal value of the amplification gain. For passive schemes our results clarify the role of squeezing in improving both the reference phase and the signal phase of an interferometer.