[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85601-en":3,"doc-seo-85601-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85601,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Optimal Quantum Differential Privacy via Fisher Information Spectral Analysis","Quantum Fisher Information (QFI) links parameter estimation accuracy and the distinguishability of quantum states, enabling a geometry-aware framework for quantum differential privacy. The approach replaces isotropic depolarizing noise with direction-dependent noise aligned to QFI eigenmodes of quantum embeddings. Six core results derive minimax-optimal mechanisms, mixed-state QFI decomposition effects, privacy–utility uncertainty bounds, adaptive QFI estimation, QFI-aligned composition, and hardware-noise privacy amplification, validated on Qiskit Aer GPU and IBM Quantum devices.","Optimal Quantum Differential Privacy via Fisher Information Spectral Analysis  \nJustice Owusu Agyemang, Jerry John Kponyo, Elliot Amponsah, and Godfred Manu Addo Boakye  \nQuantum and Assistive Technologies Lab, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana  \narXiv :2605 .24166v2 [ quant-ph] 13 Jul 2026  \nThe 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 directiondependent 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 ε = (∆2 /2)λmax (1−cγ) with O (d/λmax ) advantage; (2) mixed-state QFI decomposition reveals that dephasing in the adversary’s basis increases accessible information, while misaligned-basis dephasing provides constructive privacy amplification from hardware noise; (3) a tight privacy–utility uncertainty relation ε · (1 − F) ≥ (∆2 /2) Tr(F )/d; (4) adaptive QFI estimation converging at O(1/ √n) yields 1.92 × 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, anda 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 ε ≈ 0.001 versus ε ≈ 4800 for classical DP.  \n1 Introduction  \nThe convergence of quantum computing and machine learning has produced a rapidly advancing field encompassing quantum neural networks [1 , 2 , 3], quantum kernel methods [4 , 3 , 5], variational quantum algorithms [6 , 7], and quantum generative models [8 , 9 , 10] . These algorithms exploit quantum superposition, entanglement, and interference to achieve potential exponential speedups in classification, regression, clustering, and generative modeling tasks over their classical counterparts [11 , 12] . As these algorithms transition from theoretical constructs to cloud-accessible services on platforms such as IBM Quantum, Amazon Braket, Google Quantum AI, and IonQ, the privacy of training data and model parameters emerges as a critical concern [13 , 14 , 15] .  \nDifferential privacy (DP) [16 , 17] has become the gold standard for protecting individual privacy in classical machine learning, providing a mathematically rigorous framework that bounds the maximum information an adversary can extract about any individual training sample from the model’s outputs. Its widespread adoption in industry [18 , 19 , 20] and government applications [21] attests to its practical effectiveness. The extension of DP to quantum computation was pioneered by Aaronson and Rothblum [22], who introduced gentle measurements as a quantum analogue of the Laplace mechanism. Zhou and Ying [23] formalized quantum DP in the framework of quantum programming languages and established the depolarizing channel Φ γ(ρ) =(1 − γ)ρ + γI/d as the quantum equivalent of additive Gaussian noise, providing (ε, 0)-DP with ε = ln(1 + d(1 − Fmin)/ (γ(1 − γ))), where d is the Hilbert space dimension and Fmin the minimum pairwise fidelity of the encoded states.  \nHowever, isotropic depolarizing noise is fundamentally suboptimal for quantum machine learn-  \ning. Quantum embeddings map classical data x ∈ Rp onto a d-dimensional Hilbert space via x 7→ |ψ(x)⟩, where d = 2n for n qubits. The resulting manifold of quantum states—the complex projective space CPd−1—carries a natural Riemannian metric: the Quantum Fisher Information (QFI) [24 , 25 , 26 , 27] . This metric qua","cbCaijIHhZkpk5uv","https://ap.wps.com/l/cbCaijIHhZkpk5uv","pdf",934112,4,1,26,"English","en",105,"# Introduction\n## Quantum Fisher Information as Privacy Sensitivity\n## Geometry-Aware Quantum Differential Privacy\n## Contributions and Main Theorems","[{\"question\":\"How does the paper define quantum differential privacy using Quantum Fisher Information (QFI)?\",\"answer\":\"It uses QFI as the universal privacy sensitivity metric for quantum embeddings, aligning the applied noise with the QFI eigenstructure that captures anisotropic state distinguishability.\"},{\"question\":\"Why is QFI-aligned noise better than isotropic depolarizing noise?\",\"answer\":\"Because isotropic noise ties the privacy bound to the full Hilbert space dimension, while the proposed bound depends on the intrinsic parameter-space scale through λmax, yielding large advantage ratios for high-dimensional Hilbert spaces.\"},{\"question\":\"What do the main theoretical results establish?\",\"answer\":\"They prove a minimax-optimal noise allocation, characterize mixed-state QFI effects under adversary-basis dephasing, derive a tight privacy–utility uncertainty relation, show adaptive QFI estimation convergence, demonstrate improved composition behavior, and show hardware noise can amplify privacy.\"}]",1784204853,66,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"optimal-quantum-differential-privacy-via-fisher-information-spectral-analysis","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/optimal-quantum-differential-privacy-via-fisher-information-spectral-analysis/85601/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the paper define quantum differential privacy using Quantum Fisher Information (QFI)?","Question",{"text":75,"@type":76},"It uses QFI as the universal privacy sensitivity metric for quantum embeddings, aligning the applied noise with the QFI eigenstructure that captures anisotropic state distinguishability.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is QFI-aligned noise better than isotropic depolarizing noise?",{"text":80,"@type":76},"Because isotropic noise ties the privacy bound to the full Hilbert space dimension, while the proposed bound depends on the intrinsic parameter-space scale through λmax, yielding large advantage ratios for high-dimensional Hilbert spaces.",{"name":82,"@type":73,"acceptedAnswer":83},"What do the main theoretical results establish?",{"text":84,"@type":76},"They prove a minimax-optimal noise allocation, characterize mixed-state QFI effects under adversary-basis dephasing, derive a tight privacy–utility uncertainty relation, show adaptive QFI estimation convergence, demonstrate improved composition behavior, and show hardware noise can amplify privacy.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & 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