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Fluctuation and Noise Letters

Quantum Metrology Via Quantum Non-Gaussian States Under Noise

Sang Woo Park, Changsuk Noh, Hyunchul Nha

Published Jan 10, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0219477525400334

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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.
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.
Abstract This paper investigates the quantum features of non-Gaussian states generated by applying a two-mode squeezing operator S ˆ a b ( s ) to two generalized single-mode squeezed vacuum states (SVSs), each formed by the superposition of an SVS and a single–photon–subtracted SVS. The results show that, in the new states, the two-mode squeezing effect, the Einstein–Podolsky–Rosen (EPR) correlation, the Hillery–Zubairy entanglement, and the linear entropy are all enhanced as the two-mode squeezing parameter s increases. Moreover, both the degrees of squeezing and entanglement are improved and exceed those of the two-mode squeezed vacuum state (TMSVS) for stronger single-mode squeezing parameters. The optimal conditions for achieving such enhancements are identified for different regimes, depending on whether the generalized SVSs are purely Gaussian, maximally non-Gaussian, or intermediate states. In an application, the quantum Cramér–Rao bound (QCRB) is evaluated when the non-Gaussian states are employed as inputs to a Mach–Zehnder interferometer (MZI). The results further demonstrate that the enhanced phase sensitivity in the MZI originates from both the squeezing strengths and the intrinsic photon-subtraction operation. These findings highlight the potential of the new non-Gaussian states as promising resources for quantum metrology and quantum sensing.
We investigate the phase sensitivity of a Mach-Zehnder Interferometer (MZI) with an input of a non-Gaussian quantum entangled state, Two-Mode Photon-Subtracted Squeezed Vacuum states (TMPSSV). Parity detection is carried out at the output of the interferometer to obtain the phase uncertainty, which is a physical parameter that can quantify the sensitivity of interferometry. According to the simulation results, TMPSSV has a smaller phase uncertainty than the Two-Mode Squeezed Vacuum state (TMSV) in the entire range of the squeezing parameter which means the sensitivity of interferometry based on TMPSSV is higher than that of TMSV. Therefore, non-Gaussian entanglement based on TMPSSV provides a promising quantum resource for an ultra-sensitivity optical interferometer far beyond the standard quantum limit.
Based on the conventional Mach-Zehnder interferometer, we propose a metrological scheme to improve phase sensitivity. In this scheme, we use a coherent state and a squeezed vacuum state as input states, employ multi-photon-subtraction operations and make intensity-detection or homodyne-detection. We study phase sensitivity, quantum Fisher information and quantum Cramér-Rao bound under both ideal and lossy conditions. The results indicate that choosing an appropriate detection method and photon subtraction scheme can significantly enhance the phase sensitivity and robustness against photon losses. Even under lossy conditions, the multi-photon subtraction schemes can surpass the standard quantum limit. Notably, the homodyne detection method can even break through the Heisenberg limit. Moreover, increasing the number of photon-subtracted can enhance both phase sensitivity and quantum Fisher information. This research highlights the significant value of this scheme in quantum precision measurement.
This study investigates the use of orbital angular momentum (OAM) to enhance phase estimation in Mach-Zehnder interferometers by employing non-Gaussian states as input resources in the presence of noise. Our research demonstrates that non-Gaussian states, particularly the photon-subtraction-then-addition state, exhibit the best sensitivity in the presence of symmetric noise. Additionally, a higher order of the Bose operator of non-Gaussian states provides better sensitivity for symmetric noise. OAM can mitigate the deterioration of noise, making it possible to estimate small phase shifts $\ensuremath{\theta}\ensuremath{\rightarrow}0$. OAM enhances the resolution and sensitivity of all input states and mitigates the deterioration caused by photon loss. Additionally, OAM enhances the resolution and sensitivity of all input states, enabling the sensitivity to approach the 1/N1/N1/N limit even under significant photon loss (e.g., 5050%50 symmetric photon loss). These results hold promise for enhancing the sensitivity and robustness of quantum metrology, particularly in the presence of significant photon loss.
Abstract We propose a photon subtraction scheme within the Mach–Zehnder interferometer using a coherent state and a squeezed vacuum state as inputs. By systematically comparing intensity detection and homodyne detection methods, we demonstrate that strategically applied photon subtraction ( a -mode subtraction) significantly enhances the phase sensitivity of all detection methods. Under this configuration, homodyne detection achieves superior phase sensitivity and loss robustness compared to intensity detection. Remarkably, under 30% photon loss, the system surpasses the Heisenberg limit, enabled by the synergy among the squeezed vacuum state, non-Gaussian operations, and detection optimization. Furthermore, we quantify performance through the quantum Fisher information and the quantum Cramér-Rao bound analyses under both ideal and lossy conditions.