  In this paper, we are interested in detecting the presence of a nearby
phase-sensitive object, where traveling light works out under a low-photon loss
rate. Here we investigate the optimal quantum phase estimation with generalized
multi-component Schrodinger cat states. In addition, we show the optimal
conditions of the generalized multi-component cat states for the phase
estimation in a lossless scenario. We then demonstrate that the generalized
multi-component cat states can beat the performances of the NOON and two-mode
squeezed vacuum states in the presence of small loss, while maintaining the
quantum advantage over the standard quantum limit, attainable by coherent
states. Finally, we propose a generation scheme of the entangled
multi-component cat states with current or near-term optical technologies.
