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A quantum sensing network is used to simultaneously detect and measurephysical quantities, such as magnetic fields, at different locations. However,there is a risk that the measurement data is leaked to the third party duringthe communication. Many theoretical and experimental efforts have been made torealize a secure quantum sensing network where a high level of security isguaranteed. In this paper, we propose a protocol to estimate statisticalquantities of the target fields at different places without knowing individualvalue of the target fields. We generate an enanglement between $L$ quantumsensors, let the quantum sensor interact with local fields, and performspecific measurements on them. By calculating the quantum Fisher information toestimate the individual value of the magnetic fields, we show that we cannotobtain any information of the value of the individual fields in the limit oflarge $L$. On the other hand, in our protocol, we can estimate theoreticallyany moment of the field distribution by measuring a specific observable andevaluated relative uncertainty of $k$-th ($k=1,2,3,4$) order moment. Ourresults are a significant step towards using a quantum sensing network withsecurity inbuilt.

Anonymous estimation of intensity distribution of magnetic fields with quantum sensing network