  We propose a theoretical scheme to improve the resolution and precision of
phase measurement with parity detection in the Mach-Zehnder interferometer by
using a nonclassical input state which is generated by applying a
number-conserving generalized superposition of products (GSP) operation,
(saa^{{\dag}}+ta^{{\dag}}a)^{m} with s^2+t^2=1, on two-mode squeezed vacuum
(TMSV) state. The nonclassical properties of the proposed GSP-TMSV are
investigated via average photon number (APN), anti-bunching effect, and degrees
of two-mode squeezing. Particularly, our results show that both higher-order m
GSP operation and smaller parameter s can increase the total APN, which leads
to the improvement of quantum Fisher information. In addition, we also compare
the phase measurement precision with and without photon losses between our
scheme and the previous photon subtraction/addition schemes. It is found that
our scheme, especially for the case of s=0, has the best performance via the
enhanced phase resolution and sensitivity when comparing to those previous
schemes even in the presence of photon losses. Interestingly, without losses,
the standard quantum-noise limit (SQL) can always be surpassed in our our
scheme and the Heisenberg limit (HL) can be even achieved when s=0.5,1 with
small total APNs. However, in the presence of photon losses, the HL cannot be
beaten, but the SQL can still be overcome particularly in the large total APN
regimes. Our results here can find important applications in quantum metrology.
