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:2210.15381 · Frontiers of Physics

Quantum multiparameter estimation with multi-mode photon catalysis entangled squeezed state

Huan Zhang, Wei Ye, Shoukang Chang, Ying Xia, Liyun Hu, Zeyang Liao

Published Apr 19, 2023• 15 citations
arXivHTMLPDF

Abstract

We propose a method to generate the multi-mode entangled catalysis squeezed vacuum states (MECSVS) by embedding the cross-Kerr nonlinear medium into the Mach—Zehnder interferometer. This method realizes the exchange of quantum states between different modes based on Fredkin gate. In addition, we study the MECSVS as the probe state of multi-arm optical interferometer to realize multi-phase simultaneous estimation. The results show that the quantum Cramer—Rao bound (QCRB) of phase estimation can be improved by increasing the number of catalytic photons or decreasing the transmissivity of the optical beam splitter using for photon catalysis. In addition, we also show that even if there is photon loss, the QCRB of our photon catalysis scheme is lower than that of the ideal entangled squeezed vacuum states (ESVS), which shows that by performing the photon catalytic operation is more robust against photon loss than that without the catalytic operation. The results here can find applications in quantum metrology for multiparatmeter estimation.

DOI
10.1007/s11467-023-1274-6

Related papers

Improved phase sensitivity in a quantum optical interferometer based on multiphoton catalytic two-mode squeezed vacuum states

Huan Zhang, Wei Ye, Chaoping Wei +4 more

The usage of non-Gaussian states to improve the phase sensitivity of interferometers has been studied before. In this paper, we introduce the multiphoton catalysis two-mode squeezed vacuum (MC-TMSV) state as an input of the Mach-Zehnder interferometer (MZI) and study its phase sensitivity with photon-number parity measurement and the influence of photon losses. We also study the statistical properties of the MC-TMSV state in terms of the average photon number, the Wigner function, and the Mandel-$Q$ parameter. Our results show that the MC-TMSV state can exhibit stronger nonclassical characteristics, thereby making the phase sensitivity more precise with either the increase of the photon-catalyzed number or the decrease of the transmissivity. Furthermore, we also consider the effects of photon losses involving external- and internal-loss processes of the MZI, and we find that in both cases the sensitivity with the MC-TMSV state can be significantly better than that with the TMSV state under the same parameters especially in the serious photon losses and small initial squeezing regimes. We also find that the multiphoton catalysis is more sensitive to the external photon losses compared with the internal ones. Our results here can find important applications in quantum metrology.

Physical Review A•Jan 6, 2021•64 citations

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

Quantum multiparameter estimation with generalized balanced multimode NOON-like states

Lu Zhang, Kam Wai Clifford Chan

The simultaneous multiparameter estimation problem using a class of multimode entangled states is investigated in this paper. Specifically, the problem of optical phase imaging is considered, and the quantum probe is taken to be a balanced coherent superposition of components with an arbitrary quantum state in one mode and vacuum states in all the other modes, which is a generalization of the multimode NOON state. The analytical form for the quantum Cram\'er-Rao bound (QCRB) is presented, which shows the performance by providing a lower bound of the estimation uncertainty. It is shown that the NOON state has the worst performance among those in the class of the entangled states considered. We also analyze in detail four different scenarios, which are the NOON state, the entangled coherent state, the entangled squeezed coherent state, and the entangled squeezed vacuum state. From the comparison among these four states, we find that when the mean photon number is fixed, the squeezed vacuum state has the smallest QCRB, followed by the squeezed coherent state, entangled coherent state, and NOON state. Finally, we illustrate that the balanced entangled state can perform better than a more generalized unbalanced form studied in previous works for certain scenarios.

arXiv:1703.00063•Physical Review A•Mar 20, 2017•54 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

Nonlinear phase estimation enhanced by an actively correlated Mach-Zehnder interferometer

Gao-Feng Jiao, Keye Zhang, L. Q. Chen +2 more

A nonlinear phase shift is introduced to a Mach-Zehnder interferometer (MZI), and we present a scheme for enhancing the phase sensitivity. In our scheme, one input port of a standard MZI is injected with a coherent state and the other input port is injected with one mode of a two-mode squeezed-vacuum state. The final interference output of the MZI is detected with the method of active correlation output readout. Based on the optimal splitting ratio of beam splitters, the phase sensitivity can beat the standard quantum limit and approach the quantum Cram\'er-Rao bound. The effects of photon loss on phase sensitivity are discussed. Our scheme can also provide some estimates for units of ${\ensuremath{\chi}}^{(3)}$, due to the relation between the nonlinear phase shift and the susceptibility ${\ensuremath{\chi}}^{(3)}$ of the Kerr medium.

arXiv:2009.08059•Physical Review A•Sep 21, 2020•27 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
We propose a method to generate the multi-mode entangled catalysis squeezed vacuum states (MECSVS) by embedding the cross-Kerr nonlinear medium into the Mach—Zehnder interferometer. This method realizes the exchange of quantum states between different modes based on Fredkin gate. In addition, we study the MECSVS as the probe state of multi-arm optical interferometer to realize multi-phase simultaneous estimation. The results show that the quantum Cramer—Rao bound (QCRB) of phase estimation can be improved by increasing the number of catalytic photons or decreasing the transmissivity of the optical beam splitter using for photon catalysis. In addition, we also show that even if there is photon loss, the QCRB of our photon catalysis scheme is lower than that of the ideal entangled squeezed vacuum states (ESVS), which shows that by performing the photon catalytic operation is more robust against photon loss than that without the catalytic operation. The results here can find applications in quantum metrology for multiparatmeter estimation.
The usage of non-Gaussian states to improve the phase sensitivity of interferometers has been studied before. In this paper, we introduce the multiphoton catalysis two-mode squeezed vacuum (MC-TMSV) state as an input of the Mach-Zehnder interferometer (MZI) and study its phase sensitivity with photon-number parity measurement and the influence of photon losses. We also study the statistical properties of the MC-TMSV state in terms of the average photon number, the Wigner function, and the Mandel-QQQ parameter. Our results show that the MC-TMSV state can exhibit stronger nonclassical characteristics, thereby making the phase sensitivity more precise with either the increase of the photon-catalyzed number or the decrease of the transmissivity. Furthermore, we also consider the effects of photon losses involving external- and internal-loss processes of the MZI, and we find that in both cases the sensitivity with the MC-TMSV state can be significantly better than that with the TMSV state under the same parameters especially in the serious photon losses and small initial squeezing regimes. We also find that the multiphoton catalysis is more sensitive to the external photon losses compared with the internal ones. Our results here can find important applications in quantum metrology.
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.
The simultaneous multiparameter estimation problem using a class of multimode entangled states is investigated in this paper. Specifically, the problem of optical phase imaging is considered, and the quantum probe is taken to be a balanced coherent superposition of components with an arbitrary quantum state in one mode and vacuum states in all the other modes, which is a generalization of the multimode NOON state. The analytical form for the quantum Cram\'er-Rao bound (QCRB) is presented, which shows the performance by providing a lower bound of the estimation uncertainty. It is shown that the NOON state has the worst performance among those in the class of the entangled states considered. We also analyze in detail four different scenarios, which are the NOON state, the entangled coherent state, the entangled squeezed coherent state, and the entangled squeezed vacuum state. From the comparison among these four states, we find that when the mean photon number is fixed, the squeezed vacuum state has the smallest QCRB, followed by the squeezed coherent state, entangled coherent state, and NOON state. Finally, we illustrate that the balanced entangled state can perform better than a more generalized unbalanced form studied in previous works for certain scenarios.
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.
A nonlinear phase shift is introduced to a Mach-Zehnder interferometer (MZI), and we present a scheme for enhancing the phase sensitivity. In our scheme, one input port of a standard MZI is injected with a coherent state and the other input port is injected with one mode of a two-mode squeezed-vacuum state. The final interference output of the MZI is detected with the method of active correlation output readout. Based on the optimal splitting ratio of beam splitters, the phase sensitivity can beat the standard quantum limit and approach the quantum Cram\'er-Rao bound. The effects of photon loss on phase sensitivity are discussed. Our scheme can also provide some estimates for units of ${\ensuremath{\chi}}^{(3)}$, due to the relation between the nonlinear phase shift and the susceptibility ${\ensuremath{\chi}}^{(3)}$ of the Kerr medium.
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.