[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"branding":3,"analytics":7,"article-lean-4-library-brings-formal-proofs-to-quantum-information":10,"sections":35},{"siteName":4,"siteTagline":5,"publisherName":4,"contactEmail":6},"The Revision","Tech news, decoded.","editor@therevision.news",{"gaMeasurementId":8,"adsenseClientId":9},"G-ZW2MV82GYR","ca-pub-8533917693782264",{"article":11},{"id":12,"slug":13,"title":14,"dek":15,"body_md":16,"tags_json":17,"published_at":18,"created_at":19,"updated_at":20,"status":21,"review_note":22,"review_notes":23,"image_url":22,"persona_id":22,"persona_name":22,"section":24,"tags":25,"sources":30,"feedback":34,"feedback_at":22,"cost_usd":34,"total_tokens":34},4331,"lean-4-library-brings-formal-proofs-to-quantum-information","Lean 4 Library Brings Formal Proofs to Quantum Information","Researchers have built a Lean 4 library that machine-checks core quantum information theory results, including a proof of the data processing inequality.","A new Lean 4 library puts some of quantum information theory's foundational math under machine verification for the first time.\n\nThe library formalizes the data processing inequality for the sandwiched Rényi relative entropy — a result that bounds how much information can be lost when a quantum state passes through a channel. Researchers built a reusable framework covering quantum states, channels, tensor products, partial traces, and several operator inequality tools, all compatible with Mathlib, Lean's standard math library. The formalization also delivers strong subadditivity as a corollary and fills the last gap needed to complete a Lean proof of the generalized quantum Stein's lemma.\n\nFormal verification in mathematics has been gaining ground — most visibly with the Lean community's machine-checked proof of the polynomial Freiman-Ruzsa conjecture in 2023 — but quantum information theory has lagged behind classical areas. A machine-checkable foundation here matters because errors in quantum entropic proofs are notoriously hard to catch by hand, and these results underpin everything from quantum cryptography to error correction.\n\nThe library is positioned explicitly as infrastructure for AI-assisted research, which is the right framing: the hard part was not the AI, it was building the scaffolding rigorous enough that an AI could eventually use it without hallucinating a false lemma.","[\"quantum computing\",\"formal verification\",\"mathematics\",\"ai research\"]","2026-07-08T04:00:00.000Z","2026-07-08T06:07:46.130Z","2026-07-08T06:07:49.073Z","published",null,[],"ai",[26,27,28,29],"quantum computing","formal verification","mathematics","ai research",[31],{"name":32,"url":33},"arXiv cs.AI","https:\u002F\u002Farxiv.org\u002Fabs\u002F2607.05492",0,{"sections":36},[37,41,46,51,56,61,66,71,76,81,86,90,95,100],{"name":38,"slug":24,"count":39,"latest_published_at":40},"AI",2590,"2026-07-16T04:00:00.000Z",{"name":42,"slug":43,"count":44,"latest_published_at":45},"Security","security",294,"2026-07-15T19:59:48.000Z",{"name":47,"slug":48,"count":49,"latest_published_at":50},"Deals","deals",179,"2026-06-29T20:02:07.000Z",{"name":52,"slug":53,"count":54,"latest_published_at":55},"Policy","policy",158,"2026-07-16T00:02:48.000Z",{"name":57,"slug":58,"count":59,"latest_published_at":60},"Hardware","hardware",122,"2026-07-14T19:46:26.000Z",{"name":62,"slug":63,"count":64,"latest_published_at":65},"Consumer Tech","consumer-tech",93,"2026-07-13T13:20:48.000Z",{"name":67,"slug":68,"count":69,"latest_published_at":70},"Software","software",70,"2026-07-13T19:52:25.000Z",{"name":72,"slug":73,"count":74,"latest_published_at":75},"Science","science",66,"2026-07-10T10:29:37.000Z",{"name":77,"slug":78,"count":79,"latest_published_at":80},"Dev Tools","dev-tools",59,"2026-07-07T04:00:00.000Z",{"name":82,"slug":83,"count":84,"latest_published_at":85},"Gaming","gaming",41,"2026-07-09T04:00:00.000Z",{"name":87,"slug":88,"count":84,"latest_published_at":89},"Startups","startups","2026-06-29T20:55:50.000Z",{"name":91,"slug":92,"count":93,"latest_published_at":94},"General","general",29,"2026-07-10T22:28:58.000Z",{"name":96,"slug":97,"count":98,"latest_published_at":99},"Reviews","reviews",20,"2026-06-24T12:00:01.000Z",{"name":101,"slug":102,"count":103,"latest_published_at":104},"How-To","how-to",6,"2026-06-16T09:00:00.000Z"]