Encoding is an indispensable procedure in general phase measurement, and it is usually performed with a deterministic unitary transformation between the initial probe state and the final state. In order to improve the measurement precision, many studies focus on the optimization of the initial probe state. In this paper, we propose a scheme of subtracting one photon from the output state of an SU(1,1) interferometer. In addition to improving the output state, we find that this scheme can be used to optimize the encoding procedure. The performance of this type of optimization is only strong when the phase-sensitive negativity is induced in the Wigner function of the equivalent probe state. If a nearly perfect single-photon detector is used for the single-photon subtraction operation, the phase sensitivity within a narrow phase range can surpass $1/(\sqrt{\ensuremath{\nu}}N)$, where $N$ is the mean number of photons inside the SU(1,1) interferometer, and $\ensuremath{\nu}$ is the number of copies of the Gaussian probe state.
Encoding is an indispensable procedure in general phase measurement, and it is usually performed with a deterministic unitary transformation between the initial probe state and the final state. In order to improve the measurement precision, many studies focus on the optimization of the initial probe state. In this paper, we propose a scheme of subtracting one photon from the output state of an SU(1,1) interferometer. In addition to improving the output state, we find that this scheme can be used to optimize the encoding procedure. The performance of this type of optimization is only strong when the phase-sensitive negativity is induced in the Wigner function of the equivalent probe state. If a nearly perfect single-photon detector is used for the single-photon subtraction operation, the phase sensitivity within a narrow phase range can surpass 1/(\ensuremathνN), where N is the mean number of photons inside the SU(1,1) interferometer, and \ensuremathν is the number of copies of the Gaussian probe state.
In the field of quantum precision measurement, enhancing phase sensitivity is crucial for various applications, including quantum metrology and quantum sensing technologies. We theoretically investigate the improvement in phase sensitivity and quantum Fisher information achieved through multiphoton subtraction operations at the output port of an SU(1,1) interferometer under conditions of photon loss. We use vacuum and coherent states as the inputs and detect the outputs by intensity detection. The results indicate that internal photon losses within the SU(1,1) interferometer have a more significant impact on the phase sensitivity compared to external photon losses. Moreover, increasing the number of photon subtractions m effectively enhances both the phase sensitivity and the quantum Fisher information. Notably, even under conditions of severe photon loss, the multiphoton subtraction operations can enable the phase sensitivity to surpass the standard quantum limit, approaching both the Heisenberg limit and the quantum Cramér-Rao bound. This study provides a new theoretical basis for enhancing the phase sensitivity in the SU(1,1) interferometer.
Abstract To improve the phase sensitivity, multi-photon subtraction schemes (multi-PSS) within the SU(1,1) interferometer are proposed. The input states are the coherent state and the vacuum state, and the detection method is homodyne detection. The effects of multi-photon subtraction on phase sensitivity, quantum Fisher information (QFI), and quantum Cramér-Rao bound (QCRB) are analyzed under both ideal and photon losses situations. It is shown that the internal subtraction operation can improve the phase sensitivity, which becomes better performance by increasing subtraction number. It can also efficiently improve the robustness of the SU(1,1) interferometer against internal photon losses. By comparing separatively arbitrary photon subtraction on the two-mode inside SU(1,1) interferometer, the performance differences under different conditions are analyzed, including the asymmetric properties of non-Gaussian operations on the phase precision and the QFI. Our proposed scheme represents a valuable method for achieving quantum precision measurements.
In the field of quantum precision measurement, enhancing phase sensitivity is crucial for various applications, including quantum metrology and quantum sensing technologies. We theoretically investigate the improvement in phase sensitivity and quantum Fisher information achieved through multiphoton subtraction operations at the output port of an SU(1,1) interferometer under conditions of photon loss. We use vacuum and coherent states as the inputs and detect the outputs by intensity detection. The results indicate that internal photon losses within the SU(1,1) interferometer have a more significant impact on the phase sensitivity compared to external photon losses. Moreover, increasing the number of photon subtractions m effectively enhances both the phase sensitivity and the quantum Fisher information. Notably, even under conditions of severe photon loss, the multiphoton subtraction operations can enable the phase sensitivity to surpass the standard quantum limit, approaching both the Heisenberg limit and the quantum Cramér-Rao bound. This study provides a new theoretical basis for enhancing the phase sensitivity in the SU(1,1) interferometer.
Utilizing nonlinear elements, SU(1,1) interferometers demonstrate superior phase sensitivity compared to passive interferometers. However, the precision is significantly impacted by photon losses, particularly internal losses. We propose a theoretical scheme to improve the precision of phase measurement using homodyne detection by implementing a number-conserving operation (NCO), i.e., $a{a}^{\ifmmode\dagger\else\textdagger\fi{}}$ and ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$, inside the SU(1,1) interferometer, with the coherent state and the vacuum state as the input states. We analyze the effects of the NCO on the phase sensitivity, the quantum Fisher information (QFI), and the quantum Cram\'er-Rao bound under both ideal and photon-loss scenarios. Our findings reveal that the internal non-Gaussian operations can enhance the phase sensitivity and the QFI and effectively improve the robustness of the SU(1,1) interferometer against internal photon losses. Notably, the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme exhibits superior improvement in both the ideal and photon-loss cases in terms of phase sensitivity. Moreover, in the ideal case, the $a{a}^{\ifmmode\dagger\else\textdagger\fi{}}$ scheme slightly outperforms the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme in terms of the QFI. However, in the presence of high photon losses, the ${a}^{\ifmmode\dagger\else\textdagger\fi{}}a$ scheme demonstrates a greater advantage.
The phase sensitivity of SU(1,1) interferometer is investigated using a coherent state and an m-coherent superposition squeezed vacuum states as inputs and the intensity detection. Photon-subtraction, photon-addition and photon superposition are three special cases. Both ideal and realistic cases are considered. It is shown that the coefficient s of coherent superposition can modulate the performance of phase sensitivity, especially in a small squeezing region. Even in the presence of photon losses, the three-kind of non-Gaussian operations can achieve the improvement of measure precision, and the photon addition presents the best robustness compared to the photon subtraction and coherent superposition. For small squeezing, the first-order non-Gaussian operation may be the most preferred in improving phase sensitivity if considering the limitations of experimental conditions. Our results may be helpful for the practical application of quantum information.
A near-deterministic source of non-Gaussianity is the missing piece to reach universal and fault-tolerant quantum computing with continuous-variable optics. Due to a lack of strong non-linearities, the probabilistic photon-subtracted Gaussian states remain the most promising contender. In combination with Gaussian measurements and single-mode feed-forward operations, they have been shown to provide sufficient non-Gaussianity at high rates. However, these existing breeding protocols lack the necessary loss tolerance to be experimentally feasible. In this work, we introduce a mathematical formalism based on the application of a Gaussian blur and filter on the measured Fock Wigner function to describe general photon-subtracted Gaussian states. Within our representation, the initial squeezing, Gaussian measurements, and photon loss can all be understood as contributions to the total blurring and interchanged accordingly. We find that this intuitive approach can be used to find improvements to cat, cubic phase, and GKP state generation by compromising between success rates, feed-forward compatibility, and loss tolerance. In the case of multiple photon subtractions, this is achieved by introducing a hybrid setup variant bridging the gap between protocols based on breeding and post-selection. Finally, we establish a general lower bound on the resources needed to generate a given target state near-deterministically by introducing the expected Wigner logarithmic negativity as an additive monotone of non-Gaussianity.