Enhanced weak-value amplification with Schrödinger cat-like states

Weak-value amplification (WVA) has emerged as an effective technique for detecting extremely small physical parameters by combining weak system–meter interactions with a carefully chosen post-selection strategy. In this paper, we explore how WVA performs when the meter is prepared in a Schrödinger cat-like state (SCS). Using the Fisher information (FI) as the primary figure of merit, we assess the attainable precision in estimating the interaction parameter. We compare the sensitivities of even coherent states (ECSs), odd coherent states (OCSs), and Yurke–Stoler states (YSSs) against coherent states (CS). We demonstrate that ECS and OCS as meters provide higher FI than the CS as a meter in some cases, depending on the measurement strategy. Also, ECS yields the largest conventional FI among the four meter states. Furthermore, we explore the impact of vacuum superposition with the meter on FI. We find that optimizing the vacuum coefficient enhances the FI in some conditions. This study shows that SCSs can be useful as meter states for improving precision in weak-measurement metrology.