[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84124-en":3,"doc-seo-84124-105":30,"detail-sidebar-cat-0-en-105":92},{"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},84124,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Differentially Private Quantum Sensor Networks","Quantum sensing offers accuracy gains over classical approaches, especially for function estimation using networks of entangled sensors. When such networks measure data that must remain private, privacy mechanisms are required because entanglement can enable privacy-violating attacks. This work develops secure sensing protocols that incorporate differential privacy while maintaining Heisenberg-limited scaling. The main ann-node protocol injects noise into the sensing Hamiltonian, trading off mean-squared-error Heisenberg performance against achievable privacy.","Differentially private quantum sensor networks  \narXiv :2607 .06521v1 [ quant-ph] 7 Jul 2026  \nDaniel J. Spencer, 1, 2, 3, ∗ Kaiyan Shi, 1, 4 Emil T. Khabiboulline, 1, 2 Gorjan Alagic, 1, 4 and Alexey V. Gorshkov 1, 2  \n1 Joint Center for Quantum Information and Computer Science,  \nNIST/University of Maryland, College Park, MD 20742, USA  \n2 Joint Quantum Institute, NIST/University of Maryland, College Park, MD 20742, USA  \n3 Department of Physics, University of Maryland, College Park, MD 20742, USA  \n4 Department of Computer Science, University of Maryland, College Park, MD 20742, USA  \nQuantum sensing is a promising technology capable of demonstrating clear advantage over comparable classical techniques for precise measurement. One application of quantum sensing is in function estimation, which can be done using a network of entangled quantum sensors, allowing for measurements with greater optimal sensitivity than unentangled sensing protocols. In cases where quantum sensor networks will be used to measure data that should remain private (e.g., biomedical data), it is imperative that these protocols include a privacy mechanism to hide sensitive information. In this work, we show that entangled sensor networks are vulnerable to certain privacy-violating attacks. To mitigate these attacks, we introduce secure sensing protocols endowed with differential privacy. We reconcile differential privacy with retaining Heisenberg-limited scaling, and introduce several protocols achieving varying balances between the two. We show that our main protocol, ann-node network sensing protocol that injects noise directly into the sensing Hamiltonian, exhibits a tradeoff between the desirable O􀀀1/n2 􀀁 Heisenberg scaling of the mean-squared error of the function estimate and the level of privacy attainable. Under assumptions on the network (a common source of randomness and a constant fraction of honest parties), we show that this protocol is locally implementable and achieves (O(1),δ)-differential privacy for arbitrarily small δ while retaining Heisenberg scaling of the mean-squared error. We prove that our protocols are resilient to attacks by broad classes of classical and quantum adversaries, and find advantages in the privacy-utility tradeoff when using quantum techniques.  \nI. INTRODUCTION  \nQuantum sensing [1] is a promising technology with applications across various disciplines that rely on accurate measurements. It has been shown [2–8] that entanglement provides an advantage over unentangled protocols in networks of quantum sensors for precision measurement. In quantum sensing, a common problem of interest is function estimation, where q (θ) is a function of n parameters θ = (θ1 ,...,θn ), each coupled to a quantum sensor, which can be a qubit, a boson, or any other multi-level quantum system. The protocols proposed in, for example, Refs. [4, 6–8], solve the function estimation problem using a network of entangled qubit sensors. Physically, this function could be a magnetic or electric field to be interpolated at arbitrary positions in space. Examples of such sensor networks have been proposed for a variety of applications in geophysics [9, 10], biomedical imaging [11–16], dark matter searches [17], and the enhancement of atomic clock stability [18] .  \nOften in sensing, the figure of merit is taken to be the mean-squared error εMSE of the function estimator, in particular how εMSE scales with n, the number of sensors. The above-mentioned entangled sensing protocols achieve the desirable Heisenberg limit on εMSE , which isan improvement over the best achievable bound with any unentangled strategy, called the standard quantum limit. In this work, we restrict ourselves to linear functions of  \n∗ [djspence@umd.edu](djspence@umd.edu)  \nthe form q (θ) = P αi θi. In particular, we consider the average function, that is, we take αi = 1/n for all i = 1,..., n such that q(θ) = ~~1~~n P θi. In this scenario, the standard quantum limit on εMSE is ","cbCairqN44Bk24Jy","https://ap.wps.com/l/cbCairqN44Bk24Jy","pdf",849475,5,1,36,"English","en",105,"# Introduction\n## Quantum sensing and function estimation\n## Heisenberg vs standard quantum limits\n## Privacy requirements for sensitive sensing\n## Differencing attacks and privacy breaches","[{\"question\":\"Why are privacy mechanisms necessary in quantum sensor networks?\",\"answer\":\"Sensitive measured data (e.g., biomedical information) must remain private. Entangled sensor networks can be vulnerable to attacks that violate privacy, so protocols must explicitly include privacy mechanisms to hide sensitive information.\"},{\"question\":\"How does the work reconcile differential privacy with Heisenberg-limited scaling?\",\"answer\":\"The paper introduces differential-privacy-enhanced secure sensing protocols and shows protocols can preserve Heisenberg scaling of the mean-squared error while achieving (O(1),δ)-differential privacy for arbitrarily small δ under stated network assumptions.\"},{\"question\":\"What is the main tradeoff in the ann-node network sensing protocol?\",\"answer\":\"The ann-node protocol injects noise directly into the sensing Hamiltonian and exhibits a tradeoff between the desired O(1/n^2) Heisenberg scaling of the mean-squared error and the level of privacy attainable.\"}]",1784193113,91,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"differentially-private-quantum-sensor-networks","",{"@graph":36,"@context":86},[37,54,69],{"@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":53},"https://docshare.wps.com/document/differentially-private-quantum-sensor-networks/84124/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"Why are privacy mechanisms necessary in quantum sensor networks?","Question",{"text":76,"@type":77},"Sensitive measured data (e.g., biomedical information) must remain private. Entangled sensor networks can be vulnerable to attacks that violate privacy, so protocols must explicitly include privacy mechanisms to hide sensitive information.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the work reconcile differential privacy with Heisenberg-limited scaling?",{"text":81,"@type":77},"The paper introduces differential-privacy-enhanced secure sensing protocols and shows protocols can preserve Heisenberg scaling of the mean-squared error while achieving (O(1),δ)-differential privacy for arbitrarily small δ under stated network assumptions.",{"name":83,"@type":74,"acceptedAnswer":84},"What is the main tradeoff in the ann-node network sensing protocol?",{"text":85,"@type":77},"The ann-node protocol injects noise directly into the sensing Hamiltonian and exhibits a tradeoff between the desired O(1/n^2) Heisenberg scaling of the mean-squared error and the level of privacy attainable.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,120,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":20,"slug":138},19,"General","general"]