Entanglement-assisted cyclic weak-value-amplification metrology

Weak measurement has garnered widespread interest for its ability to amplify small physical effects at the cost of low detection probabilities. Previous entanglement and recycling techniques enhance postselection efficiency and signal-to-noise ratio (SNR) of weak measurement from distinct perspectives. Here, we incorporate a power-recycling cavity into the entanglement-assisted weak measurement system. We obtain an improvement of both detection efficiency and Fisher information, driven by the combined effects of power cycling and entanglement. Furthermore, we analyze three types of errors: cavity power loss, walk-off errors, and readout errors. The conclusions suggest that entanglement is beneficial in mitigating the effects of cavity losses. Moreover, entanglement exacerbates the walk-off effect caused by recycling, but this detriment can be balanced by proper parameter selection. Additionally, power-recycling can complement entanglement in suppressing readout noise, thus enhancing the accuracy of the measurement results and recovering the lost Fisher information. This work delves deeper into the metrological advantages of weak measurement.