Optimal Quantum Differential Privacy via Fisher Information Spectral Analysis
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Quantum Physics arXiv:2605.24166 (quant-ph) [Submitted on 22 May 2026] Title:Optimal Quantum Differential Privacy via Fisher Information Spectral Analysis Authors:Justice Owusu Agyemang, Jerry John Kponyo, Elliot Amponsah, Godfred Manu Addo Boakye View a PDF of the paper titled Optimal Quantum Differential Privacy via Fisher Information Spectral Analysis, by Justice Owusu Agyemang and 3 other authors View PDF HTML (experimental) Abstract:The Quantum Fisher Information (QFI) metric governs a fundamental duality: it quantifies both how precisely a parameter can be estimated (metrology) and how distinguishable two quantum states are (privacy). We exploit this duality to establish a geometry-aware framework for quantum differential privacy (DP) that replaces isotropic depolarizing noise with direction-dependent noise aligned to the QFI eigenstructure of the quantum embedding. We prove six principal theorems: (1) the minimax-optimal mechanism concentrates the noise budget in the dominant QFI eigenmode, achieving $\varepsilon = (\Delta^2/2)\lambda_{\max}(1-c\gamma)$ with $O(d/\lambda_{\max})$ advantage; (2) mixed-state QFI decomposition reveals that dephasing in the adversary's basis $\textit{increases}$ accessible information, while misaligned-basis dephasing provides constructive privacy amplification from hardware noise; (3) a tight privacy $-$ utility uncertainty relation $\varepsilon \cdot (1 - F) \ge \frac{\Delta^2}{2}\frac{\operatorname{Tr}(F)}{d}$; (4) adaptive QFI estimation converging at $O(1/\sqrt{n})$ yields $1.92\times$ tighter bounds; (5) QFI-aligned composition saturates at $O(1)$ versus $O(k)$ for standard composition; and (6) hardware noise can be harnessed for privacy amplification. Adversarial vulnerabilities, Wasserstein guarantees, subspace projection, and a zero-knowledge audit protocol follow as corollaries. Results are validated on Qiskit Aer GPU simulations, IBM Quantum hardware (ibm_fez, 156 qubits), and against classical DP baselines, achieving equivalent utility at $\varepsilon \approx 0.001$ versus $\varepsilon \approx 4800$ for classical DP. Subjects: Quantum Physics (quant-ph); Cryptography and Security (cs.CR) Cite as: arXiv:2605.24166 [quant-ph] (or arXiv:2605.24166v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.24166 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Justice Owusu Agyemang [view email] [v1] Fri, 22 May 2026 19:36:42 UTC (207 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal Quantum Differential Privacy via Fisher Information Spectral Analysis, by Justice Owusu Agyemang and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cs cs.CR References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)