Privacy in Distributed Quantum Sensing with Gaussian Quantum Networks

We study the privacy properties of distributed quantum sensing protocols in a Gaussian quantum network, where each node encodes a parameter via a local phase shift. For networks with more than two nodes, achieving perfect privacy is possible only asymptotically, in the limit of large photon numbers. However, we show that optimized fully symmetric Gaussian states enable improved privacy levels while maintaining near-optimal sensing performance. We show that local homodyne detection achieves a quadratic scaling of precision with the total number of photons. We further analyze the impact of thermal noise in the preparation stage on both privacy and estimation precision. Our results pave the way for the development of practical, private distributed quantum sensing protocols in continuous-variable quantum networks.