_Towards Quantum Sensor Networks

Quantum sensor networks sets a framework for distributed sensing, aimed at retrieving information from spatially separated probes using quantum resources, enhancing precision beyond classical limits. This thesis develops tools for this framework and addresses fundamental questions arising from the distributed nature of these protocols. The first question concerns the information accessible in distributed scenarios. Focusing on functions locally accessible by each party, we introduce a privacy measure ensuring that only the target function’s information is revealed. We identify entangled states that guarantee privacy under specific encoding dynamics, and find robust private states resilient to qubit loss.

We further extend these results to Hamiltonian dynamics, uncovering a mathematical structure linking private functions to private states and the nature of entanglement to the estimation of linear functions of local parameters. We proceed to employ concepts in geometry to analyze spatial quantum sensing, where sensor arrays probe an underlying field modeled by analytic functions. We transform a series of general problems into a description leveraging the linearity of the information in the distributed setting.

We provide conditions for error-free sensor placements and extend previous approaches to general least-squares estimations, illustrating advantages of entangled strategies over local ones. Next, we integrate this into quantum networks, recognizing practical constraints, such as limited quantum resources, network topology, and sensor placement. We develop a general optimization framework for designing sensing protocols that minimize estimator variance.

These methods translate sensing strategy design into linear, convex and nonconvex optimization problems, adapting to various network constraints and highlighting the impact of sensor positioning. Finally, we apply this to entangled atom gravimeters networks, establishing a proposal for the deployment of distributed gravitational field sensing, demonstrating potential for high-precision Earth interior modeling and offering a roadmap for the optimal construction and operation of quantum sensor networks, under minimal prior information.