[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81573-en":3,"doc-seo-81573-105":30,"detail-sidebar-cat-0-en-105":95},{"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},81573,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Data-Driven Learnability Transition of Measurement-Induced Entanglement","Measurement-induced entanglement (MIE) turns local measurements into long-range quantum correlations and can trigger dynamical phase transitions, yet experimental estimation is hindered by post-selection, whose cost grows exponentially with the number of measurements. This work reframes MIE detection as a data-driven learning task without prior knowledge of state preparation. Using only measurement records, a self-supervised neural network learns an uncertainty metric based on bounds of average post-measurement bipartite entanglement. For 1D all-to-all random circuits, a learnability transition emerges: polynomial resources suffice below a depth threshold, while exponential resources become necessary above it, coinciding with the breakdown of efficient classical simulation and showing signatures on noisy devices.","Data-Driven Learnability Transition of Measurement-Induced Entanglement  \narXiv :2512 .01317v3 [ quant-ph] 10 Jul 2026  \nDongheng Qian 1, 2 and Jing Wang 1, 2, 3, 4, ∗  \n1 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China  \n2 Shanghai Research Center for Quantum Sciences, Shanghai 201315, China  \n3 Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China  \n4 Hefei National Laboratory, Hefei 230088, China  \nMeasurement-induced entanglement (MIE) captures how local measurements generate long-range quantum correlations and drive dynamical phase transitions in many-body systems. Yet estimating MIE experimentally remains challenging: direct evaluation requires extensive post-selection over measurement outcomes, raising the question of whether MIE is accessible with only polynomial resources. We address this challenge by reframing MIE detection as a data-driven learning problem that assumes no prior knowledge of state preparation. Using measurement records alone, we train a neural network in a self-supervised manner to predict the uncertainty metric for MIE—the gap between upper and lower bounds of the average post-measurement bipartite entanglement. Applied to random circuits with one-dimensional all-to-all connectivity, our method reveals a learnability transition with increasing circuit depth: below a threshold the MIE can be effectively learned with resources that grow only polynomially with system size, whereas above it the required resources grow exponentially. This computational phase transition coincides with the breakdown of efficient classical simulation of the underlying quantum state. We further observe signatures of this transition on current noisy quantum devices. These results highlight the power of data-driven approaches for learning MIE and delineate the practical limits of its classical learnability.  \nQuantum entanglement is a central resource of quantum information science, enabling advantages in computation, communication, and sensing [1–5] . Importantly, entanglement need not arise solely from coherent unitary evolution: suitably chosen and adaptively processed measurements can also generate nonlocal correlations in many-body systems [6–9] . This measurement-induced entanglement (MIE) underlies measurement-based quantum computation [10], enables rapid preparation of longrange entangled states [11–15], and gives rise to novel non-equilibrium phases of matter [16–20] . In particular, in hybrid unitary–measurement dynamics, competition between scrambling and projective measurements produces a measurement-induced phase transition (MIPT), across which the scaling of MIE changes from volume law to area law [21–37] .  \nDespite its conceptual and practical significance, directly characterizing MIE in experiments remains notoriously challenging [38] . The central obstacle is postselection: probing properties of a state conditioned on a specific measurement outcome requires repeating the experiment until that outcome reoccurs, an effort that grows exponentially with the number of measurements by Born’s rule. Several scalable diagnostics have been proposed to circumvent this bottleneck, including purification of an entangled reference qubit [39–43], learnability of conserved quantities [44] or of the pre-measurement state [45], cross-entropy benchmarks [46–48] and other machine-learning proxies [49–51] . Although these proxies successfully reflect the distinct behavior of MIE in different regimes and help reveal its critical behavior, they remain indirect witnesses rather than quantitative estimators of MIE itself. Recent works have made progress showing promise and limits [52, 53] . On the one hand,  \nMIE can in principle be estimated without post-selection by leveraging quantum-classical correlations, but this requires prior knowledge of the underlying quantum dynamics and the accuracy of estimation hinges on the fideli","cbCais0myCEbwlCS","https://ap.wps.com/l/cbCais0myCEbwlCS","pdf",1370149,3,1,20,"English","en",105,"# Introduction\n## Challenges in Experimental Estimation of MIE\n## Proposed Data-Driven Learning Framework\n# Method and Learning Metric\n## Uncertainty Metric from Entanglement Bounds\n# Results: Learnability Transition and Resource Scaling\n## Polynomial vs Exponential Resource Regimes\n## Relation to Classical Simulation Breakdown\n# Robustness on Noisy Quantum Devices\n## Noise Simulations and IBM QPU Experiments","[{\"question\":\"What makes measuring measurement-induced entanglement (MIE) difficult in experiments?\",\"answer\":\"Direct MIE evaluation requires post-selection over measurement outcomes. Repeating the experiment until a specific outcome reoccurs scales exponentially with the number of measurements due to Born’s rule.\"},{\"question\":\"How does the proposed method detect MIE without post-selection or prior state knowledge?\",\"answer\":\"It treats MIE detection as a data-driven learning problem using only measurement records. A self-supervised transformer network estimates the post-measurement state on two distant qubits conditioned on an outcome, and uses an entanglement-entropy-based uncertainty metric to quantify learnability.\"},{\"question\":\"What is the key result regarding learnability as circuit depth increases?\",\"answer\":\"For random 1D all-to-all circuits, increasing depth produces a learnability transition. Below a threshold, MIE is learnable with resources growing only polynomially with system size; above it, required resources grow exponentially and the uncertainty saturates or increases.\"},{\"question\":\"How is the learnability transition connected to classical simulation and noise?\",\"answer\":\"The computational phase transition coincides with the breakdown of efficient classical simulation of the underlying quantum state. The transition also leaves observable signatures under realistic noise, including simulations and experiments on an IBM quantum processing unit.\"}]",1784174397,50,{"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":90,"head_meta":92,"extra_data":94,"updated_unix":28},"data-driven-learnability-transition-of-measurement-induced-entanglement","",{"@graph":36,"@context":89},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/data-driven-learnability-transition-of-measurement-induced-entanglement/81573/",4,{"url":51,"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",[71,77,81,85],{"name":72,"@type":73,"acceptedAnswer":74},"What makes measuring measurement-induced entanglement (MIE) difficult in experiments?","Question",{"text":75,"@type":76},"Direct MIE evaluation requires post-selection over measurement outcomes. Repeating the experiment until a specific outcome reoccurs scales exponentially with the number of measurements due to Born’s rule.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method detect MIE without post-selection or prior state knowledge?",{"text":80,"@type":76},"It treats MIE detection as a data-driven learning problem using only measurement records. A self-supervised transformer network estimates the post-measurement state on two distant qubits conditioned on an outcome, and uses an entanglement-entropy-based uncertainty metric to quantify learnability.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the key result regarding learnability as circuit depth increases?",{"text":84,"@type":76},"For random 1D all-to-all circuits, increasing depth produces a learnability transition. Below a threshold, MIE is learnable with resources growing only polynomially with system size; above it, required resources grow exponentially and the uncertainty saturates or increases.",{"name":86,"@type":73,"acceptedAnswer":87},"How is the learnability transition connected to classical simulation and noise?",{"text":88,"@type":76},"The computational phase transition coincides with the breakdown of efficient classical simulation of the underlying quantum state. The transition also leaves observable signatures under realistic noise, including simulations and experiments on an IBM quantum processing unit.","https://schema.org",{"og:url":51,"og:type":91,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":93,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":96},[97,101,105,109,114,118,123,126,130,133,137],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},"Exam",70,"exam",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},5,"Comic",60,"comic",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":29,"slug":117},6,"Technology","technology",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":124,"slug":125},30,"research-report",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":22,"slug":129},9,"Religion & Spirituality","religion-spirituality",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":22,"slug":132},"World Cup","world-cup",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":134,"slug":136},10,"Lifestyle","lifestyle",{"id":138,"doc_module":4,"doc_module_name":46,"category_name":139,"show_sort_weight":110,"slug":140},19,"General","general"]