Universal Operational Privacy in Distributed Quantum Sensing

Abstract: Privacy is a fundamental requirement in distributed quantum sensing networks, where multiple clients estimate spatially distributed parameters using shared quantum resources while interacting with potentially untrusted servers. Despite its importance, existing privacy conditions rely on idealized quantum bounds and do not fully capture the operational constraints imposed by realistic measurements. Here, we introduce a universal operational privacy framework for distributed quantum sensing, formulated in terms of the experimentally accessible classical Fisher information matrix and applicable to arbitrary protocols characterized by singular information structures. The proposed condition provides a protocol-independent criterion ensuring that no information about individual parameters is accessible to untrusted parties. We further experimentally demonstrate that a distributed quantum sensing protocol employing fewer photons than the number of estimated parameters simultaneously satisfies the universal privacy condition and achieves Heisenberg-limited precision. Our results establish universal operational constraints governing privacy in distributed quantum sensing networks and provide a foundation for practical, privacy-preserving quantum sensing beyond full-rank regimes.