Improving phase estimation using number-conserving operations

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