  The quantum remote sensing (QRS) is a scheme to add security about the
measurement results of a qubit-based sensor. A client delegates a measurement
task to a remote server that has a quantum sensor, and eavesdropper (Eve)
steals every classical information stored in the server side. By using quantum
properties, the QRS provides an asymmetricity about the information gain where
the client gets more information about the sensing results than Eve. However,
quantum states are fragile against decoherence, and so it is not clear whether
such a QRS is practically useful under the effect of realistic noise. Here, we
investigate the performance of the QRS with dephasing during the interaction
with the target fields. In the QRS, the client and server need to share a Bell
pair, and an imperfection of the Bell pair leads to a state preparation error
in a systematic way on the server side for the sensing. We consider the effect
of both dephasing and state preparation error. The uncertainty of the client
side decreases with the square root of the repetition number $M$ for small $M$,
which is the same scaling as the standard quantum metrology. On the other hand,
for large $M$, the state preparation error becomes as relevant as the
dephasing, and the uncertainty decreases logarithmically with $M$. We compare
the information gain between the client and Eve. This leads us to obtain the
conditions for the asymmetric gain to be maintained even under the effect of
dephasing.
