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

Chinese Physics B

Quantum-enhanced interferometry with unbalanced entangled coherent states

Jun Tang, Z. Z. Du, Wei Zhong, Lan 澜 Zhou 周, Yu‐Bo Sheng

Published Dec 3, 2024• 5 citations
Publisher

Abstract

Abstract We propose a quantum-enhanced metrological scheme utilizing unbalanced entangled coherent states (ECSs) generated by passing a coherent state and a coherent state superposition through an unbalanced beam splitter (BS). We identify the optimal phase sensitivity of this scheme by maximizing the quantum Fisher information (QFI) with respect to the BS transmission ratio. Our scheme outperforms the conventional scheme with a balanced BS, particularly in the presence of single-mode photon loss. Notably, our scheme retains quantum advantage in phase sensitivity in the limit of high photon intensity, where the balanced scheme offers no advantage over the classical strategy.

DOI
10.1088/1674-1056/ad99ca

Related papers

Unbalanced beam splitters enabling enhanced phase sensitivity of a Mach-Zehnder interferometer using coherent and squeezed vacuum states

Jiandong Zhang, Shuai Wang

An optical interferometer seeded by coherent and squeezed vacuum states seems to be the most promising platform for gravitational wave detection. Prior studies regarding this estimation protocol focus on the scenario in which the transmittances of two beam splitters are $\frac{1}{2}$. In this paper, with respect to the same inputs, we analyze the phase sensitivity of an unbalanced Mach-Zehnder interferometer (MZI) followed by balanced homodyne measurement. We give the optimal transmittance and demonstrate the advantage of our scheme over a balanced MZI scheme. Additionally, when the average photon number of the coherent state is dominant, the phase sensitivity of our scheme can nearly saturate the single-parameter quantum Cram\'er-Rao bound. Our results may contribute to the development of practical quantum sensing.

Physical Review A•Apr 6, 2023•14 citations

Optimal Phase Sensitivity in an Unbalanced Mach-Zehnder Interferometer

Stefan Ataman

Abstract In this work we address the problem of phase sensitivity optimization for an unbalanced Mach-Zehnder interferometer. While the quantum Fisher information can be employed in order to obtain the optimum transmission coefficient for the first beam splitter, this is no longer true for the second one, whose optimization is detection-scheme dependent. We thus consider three commonly used detection schemes and provide the optimal solution for each case. We also provide applications of the optimization method showing that for some input states a non-balanced Mach-Zehnder interferometer can outperform its balanced counterpart in terms of phase sensitivity.

Journal of Physics Conference Series•May 1, 2023•0 citations

Optimal entangled coherent states in lossy quantum-enhanced metrology

Su‐Yong Lee, Yong Sup Ihn, Zaeill Kim

We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decreases with more loss in the interferometry. Under the constraint of the input mean photon number, we obtain that the optimal entangled coherent state is more robust than a separable coherent state, even in a high photon loss rate. The optimal entangled coherent state preserves quantum advantage over the standard interferometric limit of the separable coherent state. We also show that the corresponding optimal measurement requires correlation measurement bases.

arXiv:1906.05402•Physical Review A•Jan 21, 2020•22 citations

Dose-efficient Quantum Phase Estimation in Lossy Optical Interferometry

Qilin Yu, Ben Wang, Kaimin Zheng +3 more

Optical interferometry is a cornerstone technique for precise phase measurements across various fields. In many applications, for example, biological imaging, it often necessitates stringent limits on light intensity to prevent adverse effects on light-sensitive samples, a condition known as dose-limited regimes. Maximizing the precision per dose is therefore crucial. In quantum metrology, quantum correlations enable high precision in phase estimation while adhering to dose constraints. Nevertheless, photon loss, including absorption by a sample, substantially diminishes the benefits of quantum enhancement in interferometry. In this work, we experimentally investigate a dose-efficient approach to quantum phase estimation using sequential strategies in the presence of loss. Performance of sequential strategies with and without control is evaluated through quantum Fisher information (QFI) per dose. Experimental results show that both sequential strategies exceed the classical limit and outperform the parallel strategy using unbalanced N00N states. Notably, the control-enhanced sequential strategy attains superior QFI per dose, approaching the quantum limit. These results highlight the promise of sequential strategy for imaging and sensing in resource-constrained scenarios, marking a significant step toward practical and efficient quantum metrology in lossy environments.

quant-pharXiv:2606.14254•Optica•Jun 15, 2026•0 citations

Asymmetry-enhanced phase sensing via asymmetric entangled coherent states

Xiao-Tong Chen, Rui Zhang, Wangjun Lu +3 more

We study quantum phase sensing with asymmetric two-mode entangled coherent states (ECSs) in which the two local amplitudes take different values. We find the asymmetry-enhanced phase-sensing phenomenon in which the phase-sensing sensitivity is enhanced with increasing the asymmetry in the ECSs. We indicate that the phase-sensing sensitivity can attain and even surpass the Heisenberg limit in certain regimes of parameters. We further study the effect of decoherence induced by photon loss on the phase-sensing sensitivity. It is shown that the asymmetric ECSs have greater capability against decoherence compared with the symmetric ECSs. It is indicated that the asymmetric ECSs have significant advantages over the symmetric ECSs in quantum phase sensing. We also study the practical phase-sensing scheme with the intensity-difference measurement and show that the asymmetry in the asymmetric ECSs can enhance the phase sensitivity in the practical phase-measurement scheme. Our work reveals the asymmetry in the asymmetric ECSs is a resource for quantum-enhanced sensing and may be applied to ultrasensitive quantum phase sensing in the presence of photon loss.

arXiv:2305.15865•Physical Review A•Apr 4, 2024•8 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
Abstract We propose a quantum-enhanced metrological scheme utilizing unbalanced entangled coherent states (ECSs) generated by passing a coherent state and a coherent state superposition through an unbalanced beam splitter (BS). We identify the optimal phase sensitivity of this scheme by maximizing the quantum Fisher information (QFI) with respect to the BS transmission ratio. Our scheme outperforms the conventional scheme with a balanced BS, particularly in the presence of single-mode photon loss. Notably, our scheme retains quantum advantage in phase sensitivity in the limit of high photon intensity, where the balanced scheme offers no advantage over the classical strategy.
An optical interferometer seeded by coherent and squeezed vacuum states seems to be the most promising platform for gravitational wave detection. Prior studies regarding this estimation protocol focus on the scenario in which the transmittances of two beam splitters are 12\frac{1}{2}21​. In this paper, with respect to the same inputs, we analyze the phase sensitivity of an unbalanced Mach-Zehnder interferometer (MZI) followed by balanced homodyne measurement. We give the optimal transmittance and demonstrate the advantage of our scheme over a balanced MZI scheme. Additionally, when the average photon number of the coherent state is dominant, the phase sensitivity of our scheme can nearly saturate the single-parameter quantum Cram\'er-Rao bound. Our results may contribute to the development of practical quantum sensing.
Abstract In this work we address the problem of phase sensitivity optimization for an unbalanced Mach-Zehnder interferometer. While the quantum Fisher information can be employed in order to obtain the optimum transmission coefficient for the first beam splitter, this is no longer true for the second one, whose optimization is detection-scheme dependent. We thus consider three commonly used detection schemes and provide the optimal solution for each case. We also provide applications of the optimization method showing that for some input states a non-balanced Mach-Zehnder interferometer can outperform its balanced counterpart in terms of phase sensitivity.
We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decreases with more loss in the interferometry. Under the constraint of the input mean photon number, we obtain that the optimal entangled coherent state is more robust than a separable coherent state, even in a high photon loss rate. The optimal entangled coherent state preserves quantum advantage over the standard interferometric limit of the separable coherent state. We also show that the corresponding optimal measurement requires correlation measurement bases.
Optical interferometry is a cornerstone technique for precise phase measurements across various fields. In many applications, for example, biological imaging, it often necessitates stringent limits on light intensity to prevent adverse effects on light-sensitive samples, a condition known as dose-limited regimes. Maximizing the precision per dose is therefore crucial. In quantum metrology, quantum correlations enable high precision in phase estimation while adhering to dose constraints. Nevertheless, photon loss, including absorption by a sample, substantially diminishes the benefits of quantum enhancement in interferometry. In this work, we experimentally investigate a dose-efficient approach to quantum phase estimation using sequential strategies in the presence of loss. Performance of sequential strategies with and without control is evaluated through quantum Fisher information (QFI) per dose. Experimental results show that both sequential strategies exceed the classical limit and outperform the parallel strategy using unbalanced N00N states. Notably, the control-enhanced sequential strategy attains superior QFI per dose, approaching the quantum limit. These results highlight the promise of sequential strategy for imaging and sensing in resource-constrained scenarios, marking a significant step toward practical and efficient quantum metrology in lossy environments.
We study quantum phase sensing with asymmetric two-mode entangled coherent states (ECSs) in which the two local amplitudes take different values. We find the asymmetry-enhanced phase-sensing phenomenon in which the phase-sensing sensitivity is enhanced with increasing the asymmetry in the ECSs. We indicate that the phase-sensing sensitivity can attain and even surpass the Heisenberg limit in certain regimes of parameters. We further study the effect of decoherence induced by photon loss on the phase-sensing sensitivity. It is shown that the asymmetric ECSs have greater capability against decoherence compared with the symmetric ECSs. It is indicated that the asymmetric ECSs have significant advantages over the symmetric ECSs in quantum phase sensing. We also study the practical phase-sensing scheme with the intensity-difference measurement and show that the asymmetry in the asymmetric ECSs can enhance the phase sensitivity in the practical phase-measurement scheme. Our work reveals the asymmetry in the asymmetric ECSs is a resource for quantum-enhanced sensing and may be applied to ultrasensitive quantum phase sensing in the presence of photon loss.
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.