Universal Operational Privacy in Distributed Quantum Sensing

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.

💡 Research Summary

The paper addresses the critical issue of privacy in distributed quantum sensing networks, where multiple spatially separated clients aim to estimate a global function of distributed parameters while preventing any individual parameter from being learned by untrusted servers or eavesdroppers. Existing privacy criteria rely on the rank deficiency of the quantum Fisher information matrix (QFIM), typically assuming idealized measurements and states such as GHZ‑type rank‑1 states. However, in realistic scenarios optimal measurements are often infeasible, leading to a mismatch between the QFIM and the actually accessible classical Fisher information matrix (CFIM).

To bridge this gap, the authors introduce a universal operational privacy framework that is defined directly in terms of the experimentally measurable CFIM. They propose a privacy quantifier
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