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

TL;DR

This paper introduces a secure quantum sensing network protocol that estimates statistical properties of magnetic fields across multiple locations without revealing individual field values, enhancing privacy and security.

Contribution

It proposes a novel protocol leveraging entanglement and quantum Fisher information to estimate field distribution moments securely without exposing individual measurements.

Findings

Cannot determine individual magnetic field values in large sensor networks.

The protocol can estimate any moment of the field distribution.

Achieves theoretical measurement of distribution moments with controlled uncertainty.

Abstract

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.