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

Physica Scripta

Improving phase sensitivity of a hybrid interferometer with the two-mode squeezed coherent state

Tao Shao, Pengxiang Ruan, Minyang Zhang, Yuanxiang Wang, Mingming Zhang, Qingli Jing, Jun Liu

Published Sep 18, 2024• 5 citations
Publisher

Abstract

Abstract We investigate the enhancement of phase sensitivity of a nonlinear-linear hybrid interferometer with the input of the two-mode squeezed coherent state (TMSCS). With the TMSCS produced by four-wave mixing, the quantum Cramér-Rao bounds (QCRB) can beat the Heisenberg limit (HL). Under the phase matched conditions, the optimal phase sensitivity with the balanced homodyne detection measurement can beat the HL and approach QCRB. The effects of internal and external losses on the measurement accuracy are also discussed. The results demonstrate that the scheme is robustness against to internal losses and this protocol can resist external detection loss which is up to 39%. Our results improve the performance of hybrid interferometers and this scheme can find important practical applications in quantum metrology.

DOI
10.1088/1402-4896/ad7ccf

Related papers

High-sensitivity phase estimation with a two-mode squeezed coherent state based on a Mach–Zehnder interferometer

Pengxiang Ruan, Jun Liu, Chenlu Li +3 more

Abstract A scheme is proposed based on a Mach–Zehnder interferometer with high phase sensitivity, utilizing a two-mode squeezed coherent state, generated by four-wave mixing, as input. The phase sensitivity of this scheme easily surpasses the Heisenberg limit when intensity difference detection is applied. Under phase-matching conditions, the quantum Cramér–Rao bound significantly exceeds the Heisenberg limit. Additionally, the scheme exhibits robustness against photon loss. When compared with the modified SU(1,1) interferometer with two coherent state inputs, this approach demonstrates superior measurement sensitivity, evaluated through various detection methods and the quantum Cramér–Rao bound. This work holds potential applications in quantum metrology.

Chinese Physics B•Jul 28, 2025•0 citations

The Super Phase Sensitivity of an SU(1,1) Interferometer with a Two-Mode Squeezed Coherent State via Balanced Homodyne and Intensity Detection

Changlan Xu, Lei Wang, Shaoqiu Ke +2 more

We propose a novel scheme that is used for the enhancement of phase sensitivity. The SU(1,1) interferometer with a two-mode squeezed coherent state input, using balanced homodyne detection (BHD) and intensity detection (ID), is shown. Our results demonstrate that the phase sensitivity achieved via BHD outperforms that of ID. The optimal phase sensitivity via BHD surpasses the Heisenberg limit (HL) and approaches the quantum Cramér–Rao bound. A larger photon number and parameter strength can make the phase sensitivity better. Furthermore, we show the effects of internal and external losses on phase sensitivity in detail. When external loss reaches 10%, the phase sensitivity can reach the HL. Next, we have a detailed discussion on the impact of the squeezing parameter and photon number on phase sensitivity, which shows that our scheme has better phase sensitivity and enhanced robustness. This interferometer system thus holds significant potential for applications in quantum precision measurement.

Photonics•Mar 23, 2026•0 citations

Enhancement of the phase sensitivity with two-mode squeezed coherent state based on a Mach-Zehnder interferometer

Jun Liu, Tao Shao, Yuanxiang Wang +4 more

We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.

Optics Express•Jul 26, 2023•13 citations

Deterministic sub-Heisenberg limit phase sensitivity with the squeezed coherent state via balanced homodyne detection

Chenlu Li, Shaoqiu Ke, Pengxiang Ruan +5 more

Abstract We investigate the phase sensitivities of three schemes with the input of the squeezed coherent states based on the Mach–Zehnder interferometer (MZI). With employing the balanced homodyne detection, the phase sensitivities of these schemes can surpass the shot noise limit (SNL) and reach the sub-Heisenberg limit. By adjusting the combination of the squeezing parameter and the photon number of the coherent state, both the phase sensitivities with using the balanced homodyne detection and the quantum Cramer–Rao bound can be improved. In the regime of low squeezing parameters, the scheme with the two-mode squeezed coherent state outperforms the other two schemes. The phase sensitivity can only reach the sub-SNL when the photon number is much larger. These schemes exhibit strong robustness against internal losses of the MZI and photon detector losses. This work will play an important role in the field of quantum precision measurement.

Physica Scripta•Feb 4, 2025•2 citations

Supersensitive phase estimation for hybrid interferometer using balanced homodyne detection

Tao Shao, Minyang Zhang, Chenlu Li +4 more

Abstract We have theoretically investigated the phase sensitivity of the hybrid interferometer with two coherent beams using the method of balance homodyne detection. The measurement device is a nonlinear–linear hybrid interferometer consisting of an optical parametric amplifier and a beam splitter. We prove that the phase sensitivity can beat the shot noise limit in the optimal conditions. Furthermore, we derive the quantum Cramér–Rao bound of the hybrid interferometer. The effects of transmission loss and detection loss on the measurement accuracy are discussed. The detection accuracy of this scheme is compared with that of the conventional SU (1,1) interferometer. Our results show that this scheme outperforms the conventional SU (1,1) interferometer scheme at high parametric strength. This scheme can be implemented with existing experimental techniques and will have important applications in quantum precision measurements.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 24, 2023•3 citations

Enhanced Phase Estimation via Photon-Added Two-Mode Squeezed States and Kerr Nonlinearity

Zekun Zhao, Qingqian Kang, Teng Zhao +3 more

Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.

quant-pharXiv:2602.00700•Feb 3, 2026•0 citations
Abstract We investigate the enhancement of phase sensitivity of a nonlinear-linear hybrid interferometer with the input of the two-mode squeezed coherent state (TMSCS). With the TMSCS produced by four-wave mixing, the quantum Cramér-Rao bounds (QCRB) can beat the Heisenberg limit (HL). Under the phase matched conditions, the optimal phase sensitivity with the balanced homodyne detection measurement can beat the HL and approach QCRB. The effects of internal and external losses on the measurement accuracy are also discussed. The results demonstrate that the scheme is robustness against to internal losses and this protocol can resist external detection loss which is up to 39%. Our results improve the performance of hybrid interferometers and this scheme can find important practical applications in quantum metrology.
Abstract A scheme is proposed based on a Mach–Zehnder interferometer with high phase sensitivity, utilizing a two-mode squeezed coherent state, generated by four-wave mixing, as input. The phase sensitivity of this scheme easily surpasses the Heisenberg limit when intensity difference detection is applied. Under phase-matching conditions, the quantum Cramér–Rao bound significantly exceeds the Heisenberg limit. Additionally, the scheme exhibits robustness against photon loss. When compared with the modified SU(1,1) interferometer with two coherent state inputs, this approach demonstrates superior measurement sensitivity, evaluated through various detection methods and the quantum Cramér–Rao bound. This work holds potential applications in quantum metrology.
We propose a novel scheme that is used for the enhancement of phase sensitivity. The SU(1,1) interferometer with a two-mode squeezed coherent state input, using balanced homodyne detection (BHD) and intensity detection (ID), is shown. Our results demonstrate that the phase sensitivity achieved via BHD outperforms that of ID. The optimal phase sensitivity via BHD surpasses the Heisenberg limit (HL) and approaches the quantum Cramér–Rao bound. A larger photon number and parameter strength can make the phase sensitivity better. Furthermore, we show the effects of internal and external losses on phase sensitivity in detail. When external loss reaches 10%, the phase sensitivity can reach the HL. Next, we have a detailed discussion on the impact of the squeezing parameter and photon number on phase sensitivity, which shows that our scheme has better phase sensitivity and enhanced robustness. This interferometer system thus holds significant potential for applications in quantum precision measurement.
We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.
Abstract We investigate the phase sensitivities of three schemes with the input of the squeezed coherent states based on the Mach–Zehnder interferometer (MZI). With employing the balanced homodyne detection, the phase sensitivities of these schemes can surpass the shot noise limit (SNL) and reach the sub-Heisenberg limit. By adjusting the combination of the squeezing parameter and the photon number of the coherent state, both the phase sensitivities with using the balanced homodyne detection and the quantum Cramer–Rao bound can be improved. In the regime of low squeezing parameters, the scheme with the two-mode squeezed coherent state outperforms the other two schemes. The phase sensitivity can only reach the sub-SNL when the photon number is much larger. These schemes exhibit strong robustness against internal losses of the MZI and photon detector losses. This work will play an important role in the field of quantum precision measurement.
Abstract We have theoretically investigated the phase sensitivity of the hybrid interferometer with two coherent beams using the method of balance homodyne detection. The measurement device is a nonlinear–linear hybrid interferometer consisting of an optical parametric amplifier and a beam splitter. We prove that the phase sensitivity can beat the shot noise limit in the optimal conditions. Furthermore, we derive the quantum Cramér–Rao bound of the hybrid interferometer. The effects of transmission loss and detection loss on the measurement accuracy are discussed. The detection accuracy of this scheme is compared with that of the conventional SU (1,1) interferometer. Our results show that this scheme outperforms the conventional SU (1,1) interferometer scheme at high parametric strength. This scheme can be implemented with existing experimental techniques and will have important applications in quantum precision measurements.
Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.