  Postselected weak measurement has aroused broad interest for its distinctive
ability to amplify small physical quantities. However, the low postselection
efficiency to obtain a large weak value has been a big obstacle to its
application in practice, since it may waste resources, and reduce the
measurement precision. An improved protocol was proposed in [Phys. Rev. Lett.
113, 030401 (2014)] to make the postselected weak measurement dramatically more
efficient by using entanglement. Such a protocol can increase the Fisher
information of the measurement to approximately saturate the well-known
Heisenberg limit. In this paper, we review the entanglement-assisted protocol
of postselected weak measurement in detail, and study its robustness against
technical noises. We focus on readout errors. Readout errors can greatly
degrade the performance of postselected weak measurement, especially when the
readout error probability is comparable to the postselection probability. We
show that entanglement can significantly reduce the two main detrimental
effects of readout errors: inaccuracy in the measurement result, and the loss
of Fisher information. We extend the protocol by introducing a majority vote
scheme to postselection to further compensate for readout errors. With a proper
threshold, almost no Fisher information will be lost. These results demonstrate
the effectiveness of entanglement in protecting postselected weak measurement
against readout errors.
