We theoretically explore the advantages rendered by non-Gaussian operations in phase estimation using a parity-detection-based Mach-Zehnder interferometer, with one input being a coherent state and the other being a non-Gaussian squeezed vacuum state (SVS). We consider a realistic model to perform three different non-Gaussian operations, namely, photon subtraction, photon addition, and photon catalysis on a single-mode SVS. We start by deriving the Wigner function of the non-Gaussian SVSs, which is then utilized to derive the expression for the phase sensitivity. The analysis of the phase sensitivity reveals that all three different non-Gaussian operations can enhance the phase sensitivity under suitable choices of parameters. We also consider the probabilistic nature of these non-Gaussian operations, the results of which reveal the single-photon addition to be the optimal operation. Further, our analysis also enables us to identify the optimal squeezing of the SVS and the transmissivity of the beam splitter involved in the implementation of the non-Gaussian operations.
We theoretically explore the advantages rendered by non-Gaussian operations in phase estimation using a parity-detection-based Mach-Zehnder interferometer, with one input being a coherent state and the other being a non-Gaussian squeezed vacuum state (SVS). We consider a realistic model to perform three different non-Gaussian operations, namely, photon subtraction, photon addition, and photon catalysis on a single-mode SVS. We start by deriving the Wigner function of the non-Gaussian SVSs, which is then utilized to derive the expression for the phase sensitivity. The analysis of the phase sensitivity reveals that all three different non-Gaussian operations can enhance the phase sensitivity under suitable choices of parameters. We also consider the probabilistic nature of these non-Gaussian operations, the results of which reveal the single-photon addition to be the optimal operation. Further, our analysis also enables us to identify the optimal squeezing of the SVS and the transmissivity of the beam splitter involved in the implementation of the non-Gaussian operations.
We theoretically analyze phase sensitivity using a parity-detection-based Mach-Zehnder interferometer (MZI) with the input states generated by performing non-Gaussian operations, viz., photon subtraction, photon addition, and photon catalysis, on a two-mode squeezed vacuum (TMSV) state. Since these non-Gaussian operations are probabilistic, it is of utmost importance to take the success probability into account. To this end, we consider a realistic model of photon subtraction, addition, and catalysis and derive a single expression of the Wigner function for photon subtracted, added, and catalyzed TMSV states. The Wigner function is used to evaluate the lower bound on the phase sensitivity via quantum Cram\'er-Rao bound and parity-detection-based phase sensitivity in the MZI. We identify the ranges of squeezing and transmissivity parameters where the non-Gaussian states provide better phase sensitivity than the TMSV state. Taking the success probability into account, it turns out that the photon addition is the most advantageous among all three non-Gaussian operations. We hope that the generalized Wigner function derived in this paper will be useful in various quantum information protocols and state characterization.
Abstract While the quantum metrological advantages of performing non‐Gaussian operations on two‐mode squeezed vacuum (TMSV) states have been extensively explored, similar studies in the context of two‐mode squeezed thermal (TMST) states are severely lacking. This paper explores the potential advantages of performing non‐Gaussian operations on TMST state for phase estimation using parity detection‐based Mach–Zehnder interferometry and compares it with the TMSV case. To this end, a realistic photon subtraction, addition, and catalysis model is considered. A unified Wigner function of the photon subtracted, photon added, and photon catalyzed TMST state is derived, which is used to obtain the expression for the phase sensitivity. The results show that performing non‐Gaussian operations on TMST states can enhance the phase sensitivity for significant squeezing and transmissivity parameter ranges. Because of the probabilistic nature of these operations, it is of utmost importance to consider their success probability. When the success probability is considered, the photon catalysis operation performed using a high transmissivity beam splitter is the optimal non‐Gaussian operation. This contrasts with the TMSV case, where photon addition is observed as the most optimal. Further, the derived Wigner function of the non‐Gaussian TMST states will be useful for state characterization and various quantum protocols.
We investigate the benefits of probabilistic non-Gaussian operations in phase estimation using difference-intensity and parity detection-based Mach-Zehnder interferometers (MZI). We consider an experimentally implementable model to perform three different non-Gaussian operations, namely photon subtraction (PS), photon addition (PA), and photon catalysis (PC) on a single-mode squeezed vacuum (SSV) state. In difference-intensity detection-based MZI, two PC operation is found to be the most optimal, while for parity detection-based MZI, two PA operation emerges as the most optimal process. We have also provided the corresponding squeezing and transmissivity parameters at best performance, making our study relevant for experimentalists. Further, we have derived the general expression of moment-generating function, which shall be useful in exploring other detection schemes such as homodyne detection and quadratic homodyne detection.
Abstract This study investigates the benefits of probabilistic non‐Gaussian operations in phase estimation using difference‐intensity and parity detection‐based Mach–Zehnder interferometers (MZI). An experimentally implementable model is considered to perform three different non‐Gaussian operations, namely photon subtraction (PS), photon addition (PA), and photon catalysis (PC) on a single‐mode squeezed vacuum (SSV) state. The findings reveal that all non‐Gaussian operations except one PC operation provide an advantage in either of the measurement schemes. This result is further supported by the analysis of the quantum Cramér–Rao bound. When accounting for the success probability of non‐Gaussian operations, two‐PC and four‐PA emerges as the most optimal operations in difference‐intensity and parity detection‐based MZI, respectively. Additionally, the corresponding squeezing and transmissivity parameters that yields the best performance are identified, making the study relevant for experimentalists. Furthermore, a general expression for the moment‐generating function is derived, which is useful in exploring other detection schemes such as homodyne detection and quadratic homodyne detection.
Realistic non-Gaussian operations, which can be implemented by mixing a nonclassical Gaussian state with a Fock state at a beam splitter and then heralding on a photon-number-resolving detector, are known to improve phase estimation in a Mach-Zehnder interferometer. The existing studies have considered the single-mode squeezed vacuum for difference-intensity and parity detection, and the two-mode squeezed thermal state for parity detection alone as the initial Gaussian resources. However, a real squeezer in the lab actually produces single-mode squeezed thermal light, which has not been studied in a coherent-plus-resource interferometer. We take up this case and using the phase space Wigner picture, we obtain the heralded state produced by photon subtraction, addition and catalysis on a single-mode squeezed thermal resource, and evaluate the corresponding phase sensitivities. Single-photon catalysis, which is useless on squeezed vacuum, becomes a useful operation for any thermal occupation above $\nth\simeq0.2$, and since it heralds with a probability near one-half, it turns out to be the best success-weighted operation over the whole thermal range. In the vacuum limit our results reproduce the known hierarchy, where two-photon catalysis is the best operation. The quantum Fisher information computations confirms that thermal noise enhances the phase information encoded in the catalyzed state, demonstrating that difference-intensity detection closely approaches the ultimate precision bound across most operational regimes, and, together with a loss analysis, verifies the robustness of the effect.
Non-Gaussian operations can reshape the photon statistics of continuous-variable probes, but their metrological advantage is meaningful only when heralding probability and photon-number resources are counted consistently. We compare photon subtraction, photon addition, and photon catalysis as input-side heralding operations in a balanced SU(1,1) interferometer with parity detection. A unified finite-transmissivity map supplies closed conditional moments and the corresponding quantum Fisher information at arbitrary operation order; internal loss is absorbed into a single effective parity observable whose lossless limit recovers the ideal pulled-back measurement. At fixed preparation parameters, single-photon subtraction and addition improve the conditional phase information over the Gaussian reference across most of the high-transmissivity regime, while multi-photon catalysis opens useful low-transmissivity windows. However, when the coherent--squeezed allocation is independently optimized at fixed conditional-probe energy and fixed interferometer gain, the success-weighted Fisher information of all three non-Gaussian operations remains below the optimized Gaussian benchmark. This conclusion is subject to the tested constraints: single-photon operations, a coherent-plus-squeezed-vacuum Gaussian family, fixed gain, and parity readout. Photon catalysis separately generates a conditional branch with high local quantum Fisher information that dark-point parity extracts poorly, identifying a measurement mismatch rather than a state-preparation failure. The result draws a sharp boundary between conditional non-Gaussian enhancement and practically available precision under explicitly stated resource constraints.