Abstract We consider distillation of squeezing in single mode squeezed vacuum state using three different probabilistic non-Gaussian operations: photon subtraction (PS), photon addition (PA) and photon catalysis (PC). To achieve this, we consider a practical model to implement these non-Gaussian operations and derive the Wigner characteristic function of the resulting non-Gaussian states. Our result shows that while PS and PC operations can distill squeezing, PA operation cannot. Furthermore, we delve into the success probabilities associated with these non-Gaussian operations and identify optimal parameters for the distillation of squeezing. Our current analysis holds significant relevance for experimental endeavors concerned with squeezing distillation.
Abstract We consider distillation of squeezing in single mode squeezed vacuum state using three different probabilistic non-Gaussian operations: photon subtraction (PS), photon addition (PA) and photon catalysis (PC). To achieve this, we consider a practical model to implement these non-Gaussian operations and derive the Wigner characteristic function of the resulting non-Gaussian states. Our result shows that while PS and PC operations can distill squeezing, PA operation cannot. Furthermore, we delve into the success probabilities associated with these non-Gaussian operations and identify optimal parameters for the distillation of squeezing. Our current analysis holds significant relevance for experimental endeavors concerned with squeezing distillation.
Photon subtraction (PS), due to its feasibility in physical implementation, has been widely utilized in Gaussian entanglement distillation. However, in this paper, we will show that photon addition (PA) can be employed to provide an additional enhancement in both the quality of distilled entanglement and the success probability if the input state is a weak two-mode squeezed vacuum state. Moreover, compared with biside PS, the distillation probability gains a $O(\frac{1}{{\ensuremath{\lambda}}^{2}})$ improvement, which increases rapidly when $\ensuremath{\lambda}\ensuremath{\ll}1$. Our PA-based scheme is obtained first by single-photon injection and later by vacuum state projection. The performance of PA in the presence of both an approximated single photon and amplitude-damping noise has been analyzed. Our result sheds more light on the indispensable non-Gaussian ingredients in Gaussian-state distillation and could be of great use in developing more efficient distillation schemes. Finally, the sensitivity of the PA scheme to inefficient photon detection has also been investigated.
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.
The Husimi phase distribution, an experimentally measurable quantity, is investigated for single-mode and two-mode squeezed vacuum states. The analysis highlights that non-Gaussian operations, i.e., photon subtraction (PS), photon addition (PA) and photon catalysis (PC), are effective tools for localizing phase distribution and enhancing phase robustness in the presence of noise, while PC enhances phase sensitivity but leads to greater delocalization. The work highlights the perspective that combined effects of squeezing, beam splitter transmittance, and environmental interactions must be carefully considered when quantum state engineering protocols are designed and phase properties provide a valuable insight into this endeavour.
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 Based on an asymmetrical beam splitter (ABS) and conditional measurement, we have investigated the nonclassical properties of non-Gaussian states in a unified form, including photon subtraction, photon addition and quantum catalysis, by deriving analytical expressions for photon number, squeezing effect, Mandel Q parameter and Wigner function. It is found that these properties not only depend on squeezing parameter and measurement, but also on the transmissivity of the ABS. Photon addition and quantum catalysis present a higher probability in the regions of low and high transmissivity, respectively. Although both single-photon subtraction and addition share a clear negative volume, the latter is considered to be a better choice for producing nonclassical states than the two others, if both success probability and negative volume in the small squeezing region are taken into consideration. Quantum catalysis is better in the large squeezing region and with low transmissivity. These results provide some reference for generating such non-Gaussian states.
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.