  A quantum sensing network is used to simultaneously detect and measure
physical quantities, such as magnetic fields, at different locations. However,
there is a risk that the measurement data is leaked to the third party during
the communication. Many theoretical and experimental efforts have been made to
realize a secure quantum sensing network where a high level of security is
guaranteed. In this paper, we propose a protocol to estimate statistical
quantities of the target fields at different places without knowing individual
value of the target fields. We generate an enanglement between $L$ quantum
sensors, let the quantum sensor interact with local fields, and perform
specific measurements on them. By calculating the quantum Fisher information to
estimate the individual value of the magnetic fields, we show that we cannot
obtain any information of the value of the individual fields in the limit of
large $L$. On the other hand, in our protocol, we can estimate theoretically
any moment of the field distribution by measuring a specific observable and
evaluated relative uncertainty of $k$-th ($k=1,2,3,4$) order moment. Our
results are a significant step towards using a quantum sensing network with
security inbuilt.
