Differentially private quantum sensor network protocols are introduced that inject noise into the sensing Hamiltonian, achieving (O(1), δ)-differential privacy while retaining Heisenberg-limited MSE scaling under honest-fraction and common-source-of-randomness assumptions.
Precision and Privacy in Distributed Quantum Sensing: A Quantum Fisher Information Duality
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abstract
We establish a quantum Fisher information (QFI) duality for distributed quantum sensor networks with local phase encoding. For any $N$-qubit probe state, where $N$ denotes the number of sensors, $F_Q(\boldsymbol{w}^\top \boldsymbol{\theta}) + F_Q(\boldsymbol{v}^\top \boldsymbol{\theta}) \leq N$ for all unit orthogonal sensing directions $\boldsymbol{w}$ and $\boldsymbol{v}$, with equality for all equatorial states when $N=2$ and for Greenberger--Horne--Zeilinger (GHZ) states when $N\geq 2$. Heisenberg-limited precision for direction $\boldsymbol{w}$, $F_Q(\boldsymbol{w}^\top \boldsymbol{\theta})=N$, saturates the bound and simultaneously forces zero QFI for all other independent directions. This can be interpreted as the condition for parameter privacy in distributed quantum sensing: attaining Heisenberg-limited precision for the sensing target renders all alternative privacy-intrusive estimations impossible.
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Differentially private quantum sensor networks
Differentially private quantum sensor network protocols are introduced that inject noise into the sensing Hamiltonian, achieving (O(1), δ)-differential privacy while retaining Heisenberg-limited MSE scaling under honest-fraction and common-source-of-randomness assumptions.