  A lot of attention has been paid to a quantum-sensing network for detecting
magnetic fields in different positions. Recently, cryptographic quantum
metrology was investigated where the information of the magnetic fields is
transmitted in a secure way. However, sometimes, the positions where non-zero
magnetic fields are generated could carry important information. Here, we
propose an anonymous quantum sensor where an information of positions having
non-zero magnetic fields is hidden after measuring magnetic fields with a
quantum-sensing network. Suppose that agents are located in different positions
and they have quantum sensors. After the quantum sensors are entangled, the
agents implement quantum sensing that provides a phase information if non-zero
magnetic fields exist, and POVM measurement is performed on quantum sensors.
Importantly, even if the outcomes of the POVM measurement is stolen by an
eavesdropper, information of the positions with non-zero magnetic fields is
still unknown for the eavesdropper in our protocol. In addition, we evaluate
the sensitivity of our proposed quantum sensors by using Fisher information
when there are at most two positions having non-zero magnetic fields. We show
that the sensitivity is finite unless these two (non-zero) magnetic fields have
exactly the same amplitude. Our results pave the way for new applications of
quantum-sensing network.
