The usage of non-Gaussian states to improve the phase sensitivity of interferometers has been studied before. In this paper, we introduce the multiphoton catalysis two-mode squeezed vacuum (MC-TMSV) state as an input of the Mach-Zehnder interferometer (MZI) and study its phase sensitivity with photon-number parity measurement and the influence of photon losses. We also study the statistical properties of the MC-TMSV state in terms of the average photon number, the Wigner function, and the Mandel-$Q$ parameter. Our results show that the MC-TMSV state can exhibit stronger nonclassical characteristics, thereby making the phase sensitivity more precise with either the increase of the photon-catalyzed number or the decrease of the transmissivity. Furthermore, we also consider the effects of photon losses involving external- and internal-loss processes of the MZI, and we find that in both cases the sensitivity with the MC-TMSV state can be significantly better than that with the TMSV state under the same parameters especially in the serious photon losses and small initial squeezing regimes. We also find that the multiphoton catalysis is more sensitive to the external photon losses compared with the internal ones. Our results here can find important applications in quantum metrology.
The usage of non-Gaussian states to improve the phase sensitivity of interferometers has been studied before. In this paper, we introduce the multiphoton catalysis two-mode squeezed vacuum (MC-TMSV) state as an input of the Mach-Zehnder interferometer (MZI) and study its phase sensitivity with photon-number parity measurement and the influence of photon losses. We also study the statistical properties of the MC-TMSV state in terms of the average photon number, the Wigner function, and the Mandel-Q parameter. Our results show that the MC-TMSV state can exhibit stronger nonclassical characteristics, thereby making the phase sensitivity more precise with either the increase of the photon-catalyzed number or the decrease of the transmissivity. Furthermore, we also consider the effects of photon losses involving external- and internal-loss processes of the MZI, and we find that in both cases the sensitivity with the MC-TMSV state can be significantly better than that with the TMSV state under the same parameters especially in the serious photon losses and small initial squeezing regimes. We also find that the multiphoton catalysis is more sensitive to the external photon losses compared with the internal ones. Our results here can find important applications in quantum metrology.
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.
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.
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 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.
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.
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.
Quantum metrology is to estimate accurately the value of an unknown parameter with the assistance of the quantum effects, in order to break through the standard quantum limit, even reach the Heisenberg limit. In this work, we study the performance of a general photon-added two-mode squeezed vacuum state that is taken as a detection state of a Mach-Zehnder interferometer. Based on quantum Fisher information, within the constraint on the total mean photon number, symmetric and asymmetric photon addition cannot improve the ultimate phase sensitivity. However, for a given initial squeezing parameter, on this occasion, the symmetric and asymmetric photon addition can improve the ultimate phase sensitivity. Compared with the asymmetric photon-added two-mode squeezed vacuum state, the symmetric one can well improve the ultimate phase sensitivity. This may be because it is always better to implement the symmetric photon addition rather than the asymmetric one in order to increase the mean photon number of the resulting state. On the other hand, via parity detection, the symmetric and asymmetric photon-added two-mode squeezed vacuum state can indeed improve the phase sensitivity of a Mach-Zehnder interferometer for a given initial squeezing parameter. Based on the parity detection, within a constraint on the mean photon number, although the two-mode squeezed vacuum state can give the better phase sensitivity at the optimal phase shift (φ = 0), the phase sensitivity offered by the symmetric and asymmetric photon-added two-mode squeezed vacuum states are both more stable around φ = 0 than by the two-mode squeezed vacuum state. In addition, we show that for the symmetric photon-added two-mode squeezed vacuum state, parity detection is an optimal detection only when the optimal phase shift approaches to zero. When the phase shift slightly deviates from zero, the parity detection is not an optimal detection scheme. Finally, for all values of the phase shift, our results also clearly show that the parity detection is not an optimal detection scheme for the asymmetric photon-added two-mode squeezed vacuum state serving as an interferometer state.