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.
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.
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.
Non-Gaussian operations have been studied intensively in recent years due to their ability to enhance the entanglement of quantum states. However, most previous studies on such operations are carried out in a single-mode setting, even though in reality any quantum state contains multi-mode components in frequency space. Whilst there have been general frameworks developed for multi-mode photon subtraction (PS) and photon addition (PA), an important gap exists in that no framework has thus far been developed for multi-mode photon catalysis (PC). In this work we close that gap. We then apply our newly developed PC framework to the problem of continuous variable (CV) entanglement distribution via quantum-enabled satellites. Due to the high pulse rate envisioned for such systems, multi-mode effects will be to the fore in space-based CV deployments. After determining the entanglement distribution possible via multi-mode PC, we then compare our results with the entanglement distribution possible using multi-mode PS and PA. Our results show that multi-mode PC carried out at the transmitter is the superior non-Gaussian operation for certain regions of the parameter space. The size of this region is highly dependent on the squeezing of the initial state. When carried out at the receiver, multi-mode PC is again found to be the superior non-Gaussian operation for certain regions of the parameter space. In this latter region, the region size is more dependent on the channel loss. Our new results should prove valuable for next-generation deployments of CV quantum-enabled satellites.
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.
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.
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.
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.