  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.
