  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, and find that the improvement from entanglement and
recycling occur in different dimensions. Furthermore, we analyze two types of
errors, walk-off errors and readout errors. The conclusions suggest that
entanglement exacerbates the walk-off effect caused by recycling, but this
detriment can be balanced by proper parameter selection. In addition,
power-recycling can complement entanglement in suppressing readout noise, thus
enhancing the accuracy in the measurement results and recovering the lost
Fisher information. This work delves deeper into the metrological advantages of
weak measurement.
