Santiago Scheiner

Quantum sensors are powerful tools for measuring physical quantities with high sensitivity, enabling, for instance, the mapping of Earth’s gravitational field , detecting very small changes of magnetic fields, or the passage of time. The underlying principle is to use a quantum state as a probe that interacts with the physical quantity of interest, thereby encoding relevant information into the state. Although individual quantum sensors may exhibit remarkable sensitivity, the precision of a certain measurement can be significantly enhanced when multiple probes are entangled. Distributed quantum sensing extends this further and leverages entanglement among spatially separated sensors, allowing them to function as a single, coherent system. This approach enables measurements across extended spatial regions, while surpassing the precision achievable by independent sensors. However, a significant challenge in a network setting is ensuring that sensors deployed across different parties serve as the necessary resources for the correct functioning of the target sensing task. This challenge has motivated the combination of quantum cryptography with quantum sensing. In this context, Shettell et al. introduced the notion of privacy for sensor networks, ensuring that, beyond the metrological advantage of cooperative estimation of a global function, parties can also maintain the privacy of their local information and control what data is accessible to others. In this work, we adopt this protocol and focus on a multi-user quantum sensor network framework to analyze the privacy aspects of this parameter estimation task, leveraging a high-quality four-party GHZ state source.

Quantum networks have recently generated significant interest due to enhanced functionalities and security, including offering the capability to securely calculate a linear function of several parameters which themselves remain private. This allows joint estimation of a parameter using the precision advantage of quantum sensing. In this work, we extend the functionality of previously considered schemes to allow for some subset of the network, without sharing their own private network, to carry out parameter estimation together without revealing the identities of participants, either to each other or to the rest of the network, while being guaranteed that only the relevant parties have inputted their parameter.