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.
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.
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.
Abstract To improve the phase sensitivity, multi-photon subtraction schemes (multi-PSS) within the SU(1,1) interferometer are proposed. The input states are the coherent state and the vacuum state, and the detection method is homodyne detection. The effects of multi-photon subtraction on phase sensitivity, quantum Fisher information (QFI), and quantum Cramér-Rao bound (QCRB) are analyzed under both ideal and photon losses situations. It is shown that the internal subtraction operation can improve the phase sensitivity, which becomes better performance by increasing subtraction number. It can also efficiently improve the robustness of the SU(1,1) interferometer against internal photon losses. By comparing separatively arbitrary photon subtraction on the two-mode inside SU(1,1) interferometer, the performance differences under different conditions are analyzed, including the asymmetric properties of non-Gaussian operations on the phase precision and the QFI. Our proposed scheme represents a valuable method for achieving quantum precision measurements.
The hybrid interferometer, integrating an optical parametric amplifier and a beam splitter, exhibits the potential to outperform the SU(1,1) interferometer. However, photon loss remains a key constraint for practical implementation. To address this challenge, we propose a quantum metrology scheme that utilizes multi-photon subtraction at the output and replaces the standard 50:50 beam splitter with a variable beam splitter—thereby enhancing robustness to photon loss. We adopt a coherent state (injected into mode a or b ) and a vacuum state as inputs to the interferometer, while performing homodyne detection. Our results demonstrate that the selection of input modes exerts a significant influence on phase estimation, and the optimization of the beam splitter’s transmittance is essential to maximize phase sensitivity under lossy conditions. Furthermore, photon subtraction notably enhances phase sensitivity, quantum Fisher information, and noise robustness. Notably, our scheme attains sensitivities exceeding the Heisenberg limit even in the presence of 20% photon loss.
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} as a comparative figure of merit within the SLD/RLD framework. We find that parametric amplification can substantially reduce the most informative bound, BMI, thereby enhancing multiparameter estimation precision over a broad range of operating conditions. Coherent feedback can further reduce 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 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 metrology aims to achieve measurement precision that surpasses classical limits in the estimation of physical parameters. In realistic conditions, however, its advantage can be diminished by interactions between a quantum system and its environment. This necessitates careful design of quantum resources that can sustain enhanced performance even under noise. Here, we investigate how a quantum non-Gaussian operation can provide an advantage in noisy quantum metrology. Specifically, we examine the effect of single-photon subtraction applied to a two-mode squeezed vacuum state in the task of phase estimation using a Mach–Zehnder interferometer under photon loss. The single-photon subtraction can be implemented either before or after the first beam splitter in the interferometer. By evaluating the quantum Fisher information for both the original and the photon-subtracted states, we assess the potential enhancement in sensing precision. We show that the enhancement occurs when photon subtraction is performed before the first beam splitter, provided that loss acts only on the signal mode. Our findings shed light on the role of non-Gaussian operations in noisy quantum metrology, clarifying when photon subtraction can yield a genuine advantage over Gaussian resources.