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Precision and Privacy in Distributed Quantum Sensing: A Quantum Fisher Information Duality

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arXiv:2605.20765v1 Announce Type: cross 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--

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Quantum Physics [Submitted on 20 May 2026] Precision and Privacy in Distributed Quantum Sensing: A Quantum Fisher Information Duality Farhad Farokhi 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. Subjects: Quantum Physics (quant-ph); Cryptography and Security (cs.CR); Information Theory (cs.IT) Cite as: arXiv:2605.20765 [quant-ph] (or arXiv:2605.20765v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.20765 Focus to learn more Submission history From: Farhad Farokhi [view email] [v1] Wed, 20 May 2026 06:07:19 UTC (12 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev | next > new | recent | 2026-05 Change to browse by: cs cs.CR cs.IT math math.IT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

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