Abstract The precision of quantum measurements can be effectively improved by using both photon-added non-Gaussian operations and Kerr nonlinear phase shift. Here, we employ a coherent state mixed with a photon-added squeezed vacuum state as the input to a Mach–Zehnder interferometer with parity detection, thereby achieving a significant enhancement in phase measurement precision. Our research focuses on the phase sensitivity of linear phase shift under both ideal conditions and photon loss, as well as quantum Fisher information (QFI). The results demonstrate that employing the photon addition operations can markedly enhance phase sensitivity and QFI, and under optimal conditions, the measurement precision can approach the Heisenberg limit for the linear phase shift case. In addition, we delve deeper into the scenario of replacing the linear phase shift with a Kerr nonlinear one and systematically analyze the QFI under both ideal and photon loss conditions. By comparison, it is evident that employing both the photon addition operations and the Kerr nonlinear phase shift can further significantly enhance phase measurement precision while effectively improving the system’s robustness against photon loss. These findings are instrumental in facilitating the development and practical application of quantum metrology.
Abstract The precision of quantum measurements can be effectively improved by using both photon-added non-Gaussian operations and Kerr nonlinear phase shift. Here, we employ a coherent state mixed with a photon-added squeezed vacuum state as the input to a Mach–Zehnder interferometer with parity detection, thereby achieving a significant enhancement in phase measurement precision. Our research focuses on the phase sensitivity of linear phase shift under both ideal conditions and photon loss, as well as quantum Fisher information (QFI). The results demonstrate that employing the photon addition operations can markedly enhance phase sensitivity and QFI, and under optimal conditions, the measurement precision can approach the Heisenberg limit for the linear phase shift case. In addition, we delve deeper into the scenario of replacing the linear phase shift with a Kerr nonlinear one and systematically analyze the QFI under both ideal and photon loss conditions. By comparison, it is evident that employing both the photon addition operations and the Kerr nonlinear phase shift can further significantly enhance phase measurement precision while effectively improving the system’s robustness against photon loss. These findings are instrumental in facilitating the development and practical application of quantum metrology.
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.
We propose a high-precision phase estimation scheme in a hybrid interferometer by synergistically combining a Kerr nonlinear phase shifter and multi-photon subtraction operations. Using a coherent state and a vacuum state as input resources, we systematically evaluate the phase sensitivity via homodyne detection and analyze the quantum Fisher information as well as the quantum Cramér-Rao bound under both ideal and lossy conditions. Our results show that the joint integration of Kerr nonlinearity and multi-photon subtraction yields remarkable advantages over either technique used alone. The proposed scheme enables the phase sensitivity to surpass the standard quantum limit, exceed the conventional Heisenberg scaling (1/N), and approach the super-Heisenberg scaling (1/N2)-a direct consequence of Kerr nonlinearity. More precisely, the super-Heisenberg scaling $\propto $ 1/N2 is the ultimate precision limit permitted by the k=2 Kerr nonlinearity and does not violate the fundamental Heisenberg limit for linear phase accumulation. Even under moderate internal photon loss, the system maintains high precision and exhibits enhanced robustness to decoherence. The Kerr nonlinearity introduces an intensity-dependent phase shift proportional to the squared photon number, while multi-photon subtraction tailors non-Gaussian states to strengthen phase information extraction. Compared with existing schemes based on hybrid interferometers or SU(1,1) interferometers, our architecture achieves superior precision and stronger loss resilience. All components are experimentally accessible with current quantum optical technologies. This work provides a promising route for practical high-precision quantum metrology and quantum sensing.
ABSTRACT Photon addition operations applied to squeezed states have been shown to significantly enhance phase sensitivity. In this work, we extend this approach by applying photon addition not only to coherent states but also within a Mach–Zehnder interferometer, using coherent and squeezed vacuum states as input. Both intensity‐difference and homodyne detection are used to evaluate photon addition schemes, and their phase sensitivities are compared under ideal and lossy conditions. We also analyze the quantum Fisher information of these two schemes. Results show that both schemes improve phase sensitivity, quantum Fisher information, and robustness against losses. In particular, photon addition within the interferometer performs better. Homodyne detection outperforms intensity difference detection under photon losses. Notably, the two schemes exhibit distinct parameter dependencies, rendering them suitable for different operational scenarios. When the squeezing parameter is small, photon addition employed at the coherent input with intensity difference detection can approach the Heisenberg limit in ideal conditions and can exceed the standard quantum limit in high‐loss conditions. The proposed scheme represents a valuable method for quantum precision measurements. PACS : 03.67.‐a, 05.30.‐d, 42.50,Dv, 03.65.Wj
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.
The research focused on enhancing the measurement accuracy through the use of non-Gaussian states has garnered increasing attention. In this study, we propose a scheme to input the coherent state mixed with a photon-catalyzed squeezed vacuum state into the Mach-Zender interferometer to enhance phase measurement accuracy. The findings demonstrate that photon catalysis, particularly multi-photon catalysis, can effectively improve the phase sensitivity of parity detection and the quantum Fisher information. Moreover, the situation of photon losses in practical measurement was studied. The results indicate that external dissipation has a greater influence on phase sensitivity than the internal dissipation. Compared to input coherent state mixed with squeezed vacuum state, the utilization of coherent state mixed photon-catalyzed squeezed vacuum state, particularly the mixed multi-photon catalyzed squeezed vacuum state as input, can enhance the phase sensitivity and quantum Fisher information. Furthermore, the phase measurement accuracy can exceed the standard quantum limit, and even surpass the Heisenberg limit. This research is expected to significantly contribute to quantum precision measurement.
For the precision-based measurements, Mach-Zehnder interferometry is a widely used technique. There are various ways to enhance the precision of Mach-Zehnder interferometer (MZI), e.g., having a non-classical input state is one of the ways to enhance the precision of the phase estimation performed by MZI. The phase estimation performed by MZI is investigated here by considering that the input states of MZI are different combinations of photon added and subtracted squeezed coherent states (PASCS and PSSCS). Using quantum Fisher information, it is shown that the use of PASCS in both the input modes of MZI, provides the most precise estimate of the unknown phase. This system is also analyzed in two different measurement scenarios -- single intensity detection (SID) and intensity difference detection (IDD). Systematic analysis has established that the intensity measurement might not be an optimal measurement scheme for phase estimation in MZI as phase and intensity correspond to non-commuting observables. The impact of the photon loss on the MZI-based phase estimation setup is also studied and it is found that PASCS is robust against photon loss, when the loss in MZI is low.