We investigate the sensitivity of phase estimation in a Mach–Zehnder interferometer with photon-subtracted two-mode squeezed vacuum states. Our results show that, for given initial squeezing parameter, both symmetric and asymmetric photon subtractions can further improve the quantum Cramér–Rao bound (i.e., the ultimate phase sensitivity), especially for single-mode photon subtraction. On the other hand, the quantum Cramér–Rao bound can be reached by parity detection for symmetric photon-subtracted two-mode squeezed vacuum states at particular values of the phase shift, but it is not valid for asymmetric photon-subtracted two-mode squeezed vacuum states. In addition, compared with the two-mode squeezed vacuum state, the phase sensitivity via parity detection with asymmetric photon-subtracted two-mode squeezed vacuum states will be getting worse. Thus, parity detection may not always be the optimal detection scheme for nonclassical states of light when they are considered as the interferometer states.
We theoretically derive the lower and upper bounds of quantum Fisher information (QFI) of an SU(1,1) interferometer whatever the input state chosen. According to the QFI, the crucial resource for quantum enhancement is shown to be large intramode correlations indicated by the Mandel
Q parameter. The subtraction of photons from the squeezed vacuum state has the effect of increasing the average photon number of the new field state, as well as the intramode correlations. For example, for a coherent state $\ensuremath{\bigotimes}$ a squeezed vacuum state with a given fixed input mean number of photons as the input, if
p photons are subtracted from the squeezed-vacuum state before inputting the SU(1,1) interferometer, the phase sensitivities can be improved due to the intramode-correlation increment.
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.