Quantum-Enhanced Phase Estimation with Photon-Added Even and Odd Coherent States in an SU(1,1) Interferometer

Abstract

We investigate phase estimation in an SU(1,1) interferometer employing $m$-photon-added even and odd coherent states as nonclassical input resources. The phase sensitivity is evaluated through intensity detection and the error propagation method, while the ultimate precision limit is determined from the quantum Cram\'er-Rao bound with the quantum Fisher information serving as the relevant metrological quantity. Our results demonstrate that photon addition significantly enhances the phase sensitivity, increases the quantum Fisher information, and reduces the quantum Cram\'er-Rao bound, leading to a clear improvement over the corresponding even and odd coherent states. Furthermore, the achievable sensitivity exceeds the standard quantum limit and gradually approaches the Heisenberg scaling with increasing photon-addition number. We also find that the $m$-photon-added even coherent states exhibit a modest advantage over their odd counterparts. As $m$ increases, however, this distinction becomes progressively weaker, suggesting that photon addition diminishes the role of the initial parity of the coherent state in determining the interferometric performance.