[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82325-en":3,"doc-seo-82325-105":29,"detail-sidebar-cat-0-en-105":89},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82325,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","When Routes Run Out: Adversarial Co-Learning and Explainable Robustness in Quantum Repeater Networks","Study of an adversarial bandit game for entanglement-based routing in quantum repeater networks using an Ekert-91 (E91) protocol. Alice selects end-to-end repeater routes while Eve chooses an attack surface, modeled as edge intercept–resend or repeater memory degradation. Payoffs come from cached SeQUeNCe-simulated E91 transcripts with CHSH-gated acceptance. Adversarial co-learning across 50 structured topologies yields learned retention tracking a full-matrix minimax reference (Pearson r = 0.99). Decision-tree explanations are evaluated by faithfulness, then distilled via prompt records for local language models to build an open-source explanation workflow for these network games.","When Routes Run Out: Adversarial Co-Learning and Explainable Robustness in Quantum Repeater  \nNetworks  \nBrennan Bell∗ , Inti Gabriel Mendoza Estrada†, Andreas Tr¨ugler‡, and Paul Erker§  \narXiv :2607 .09378v1 [ quant-ph] 10 Jul 2026  \nAbstract—We study an adversarial bandit problem for entanglement-based quantum-network routing over a modest graph corpus. Alice selects an end-to-end repeater route for an Ekert-91 protocol (E91) representing her move, while Eve selectsan attack surface, either edge intercept–resend or repeater memory degradation. Payoffs are drawn from cached SeQUeNCesimulated E91 transcripts, and Alice accepts a turn when the finite-sample statistic violates the Clauser-Horne-Shimony-Holt (CHSH) bound. Performing adversarial co-learning across 50 structured topologies, we find that learned retention tracks a full-matrix minimax reference closely (Pearson r = 0 .99): under a one-surface Eve action model, bottleneck families have zero retention, while non-bottleneck families follow a 1−1/N coverage principle. We then fit decision-tree explanation models to graph-, attack-, and route-level topology-corpus targets and report their faithfulness. Finally, we construct prompt records for local language models to summarize the tree evidence, resulting in an open-source explanation workflow for quantum-repeater network games.  \nIndex Terms—quantum, E91, CHSH, adversarial, Exp3, bandits, games, networks, repeaters, XAI, simulations, security  \nI. INTRODUCTION  \nA. Research questions  \nThe present works analyses two main questions. Can a standard adversarial bandit, playing from bandit feedback with no topology knowledge, recover the strategic structure of route selection and attack placement in a simulated Ekert-91 (E91) repeater network? Can the learned and reference strategies then be explained—by symbolic representations and small local language models—with measured faithfulness and without security-oriented hallucinations?  \nB. Motivation  \nIn E91, Alice and Bob consume entangled pairs and use Bell-test statistics as a security monitor [1], [2], [3] . On a repeater network, route choice also induces a classical interdiction game: Alice’s mixed strategy determines which fibers and memories are exposed, while a limited Eve chooses one component to attack. This route-versus-surface structure  \nis well known in zero-sum network interdiction [4] . In the ∗ RFI-IRFOS and TU Graz, Graz, Austria; [bell.brennan.p@gmail.com](bell.brennan.p@gmail.com)[ ](bell.brennan.p@gmail.com)†openmaind FlexCo and TU Graz, Graz, Austria;  \ninti.mendoza@openmaind.ai  \n‡Know Center Research GmbH and University of Graz, Graz, Austria; [andreas.truegler@uni-graz.at](andreas.truegler@uni-graz.at)  \n§ Atominstitut, TU Wien and IQOQI, ¨OAW, Vienna, Austria; [paul.erker@tuwien.ac.at](paul.erker@tuwien.ac.at)  \nhomogeneous case, a component on every Alice–Bob route exposes a fatal bottleneck to Eve, i.e. with N componentdisjoint routes and one attacked surface, uniform routing gives hit probability 1/N, hence a retention of 1 − 1/N.  \nThe question is therefore not whether an algorithm can rediscover this coverage logic in a binary graph game. It is whether the same strategic structure remains visible when payoffs are generated by topology-corpus E91 transcripts: CHSHgated acceptance, shared repeater memories, unattacked failures, and component attacks. Explanations matter because simulator diagnostics are easy to over-interpret as quantum key distribution (QKD) security claims.  \nC. Related work  \nSeQUeNCe and NetSquid make quantum-network hardware and control assumptions explicit [5], [6]; recent trappedion network nodes motivate high-efficiency parameter scales [7] . Exponential-weight algorithm for Exploration and Exploitation (Exp3) is the standard adversarial bandit [8]; in zero-sum games, no-regret learning supports time-averaged strategies, while terminal multiplicative-weight iterates may fail to converge [9], [10] . For explanation, we use","cbCaituHhzm2qU8V","https://ap.wps.com/l/cbCaituHhzm2qU8V","pdf",445878,1,4,"English","en",105,"# Introduction\n## Research questions\n## Motivation\n## Related work\n# Modeling and Methodology\n## Quantum repeater network simulation\n## Minimax reference and Exp3","[{\"question\":\"What is the adversarial bandit setting studied for quantum repeater routing?\",\"answer\":\"Alice chooses an end-to-end repeater route for an E91 (Ekert-91) communication protocol, while Eve selects an attack surface, such as edge intercept–resend or repeater memory degradation. Payoffs are based on cached simulated E91 transcripts with CHSH-gated acceptance.\"},{\"question\":\"How is routing performance compared against a reference strategy?\",\"answer\":\"A full-matrix minimax reference is computed from the cached payoff structure, then learned averaged strategies are evaluated relative to the Nash equilibrium gap. Learned retention is reported to closely match the minimax reference across 50 structured topologies.\"},{\"question\":\"How are the learned strategies explained and validated?\",\"answer\":\"The work fits shallow decision-tree models targeting graph-, attack-, and route-level objectives and measures their faithfulness. It then constructs prompt records for local language models to summarize the decision-tree evidence using an open-source explanation workflow.\"}]",1784179640,10,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":84,"head_meta":86,"extra_data":88,"updated_unix":27},"when-routes-run-out-adversarial-co-learning-and-explainable-robustness-in-quantum-repeater-networks","",{"@graph":35,"@context":83},[36,52,66],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":21},"https://docshare.wps.com/document/when-routes-run-out-adversarial-co-learning-and-explainable-robustness-in-quantum-repeater-networks/82325/",{"url":51,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":23,"description":14,"dateModified":60,"datePublished":60,"encodingFormat":59,"isAccessibleForFree":61,"interactionStatistic":62},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":40,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":63,"interactionType":64,"userInteractionCount":4},"InteractionCounter",{"@type":65},"ViewAction",{"@type":67,"mainEntity":68},"FAQPage",[69,75,79],{"name":70,"@type":71,"acceptedAnswer":72},"What is the adversarial bandit setting studied for quantum repeater routing?","Question",{"text":73,"@type":74},"Alice chooses an end-to-end repeater route for an E91 (Ekert-91) communication protocol, while Eve selects an attack surface, such as edge intercept–resend or repeater memory degradation. Payoffs are based on cached simulated E91 transcripts with CHSH-gated acceptance.","Answer",{"name":76,"@type":71,"acceptedAnswer":77},"How is routing performance compared against a reference strategy?",{"text":78,"@type":74},"A full-matrix minimax reference is computed from the cached payoff structure, then learned averaged strategies are evaluated relative to the Nash equilibrium gap. Learned retention is reported to closely match the minimax reference across 50 structured topologies.",{"name":80,"@type":71,"acceptedAnswer":81},"How are the learned strategies explained and validated?",{"text":82,"@type":74},"The work fits shallow decision-tree models targeting graph-, attack-, and route-level objectives and measures their faithfulness. It then constructs prompt records for local language models to summarize the decision-tree evidence using an open-source explanation workflow.","https://schema.org",{"og:url":51,"og:type":85,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":87,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":90},[91,95,99,103,108,113,118,121,126,129,132],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":92,"show_sort_weight":93,"slug":94},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":96,"show_sort_weight":97,"slug":98},"Literature",80,"literature",{"id":21,"doc_module":4,"doc_module_name":45,"category_name":100,"show_sort_weight":101,"slug":102},"Exam",70,"exam",{"id":104,"doc_module":4,"doc_module_name":45,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":109,"doc_module":4,"doc_module_name":45,"category_name":110,"show_sort_weight":111,"slug":112},6,"Technology",50,"technology",{"id":114,"doc_module":4,"doc_module_name":45,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":119,"slug":120},30,"research-report",{"id":122,"doc_module":4,"doc_module_name":45,"category_name":123,"show_sort_weight":124,"slug":125},9,"Religion & Spirituality",20,"religion-spirituality",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":127,"show_sort_weight":124,"slug":128},"World Cup","world-cup",{"id":28,"doc_module":4,"doc_module_name":45,"category_name":130,"show_sort_weight":28,"slug":131},"Lifestyle","lifestyle",{"id":133,"doc_module":4,"doc_module_name":45,"category_name":134,"show_sort_weight":104,"slug":135},19,"General","general"]