Improving phase estimation using the number-conserving operations

TL;DR

This paper introduces a theoretical scheme using a number-conserving operation on two-mode squeezed vacuum states to enhance phase measurement resolution and sensitivity in quantum metrology, outperforming previous methods especially under photon loss conditions.

Contribution

The paper proposes a novel GSP operation-based method to improve phase estimation precision, surpassing previous schemes and achieving Heisenberg limit under ideal conditions.

Findings

Higher-order GSP operation increases photon number and Fisher information.

Scheme surpasses standard quantum limit and approaches Heisenberg limit.

Performance remains robust under photon losses, especially at high photon numbers.

Abstract

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.