{"schema":"postcutoff/event@1","as_of":"2026-10-12T22:30:00+02:00","url":"https://postcutoff.com/e/2026-10-08-ppt-entanglement-distillation-rains-bound-chatgpt-astra/","md":"https://postcutoff.com/e/2026-10-08-ppt-entanglement-distillation-rains-bound-chatgpt-astra/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"Adam Bicz","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-10-08-ppt-entanglement-distillation-rains-bound-chatgpt-astra","date":"2026-10-08","date_precision":"day","short_title":"PPT-distillable entanglement can fall strictly below the regularised Rains bound","deck":"Results \"derived almost entirely by ChatGPT Astra\" (Lami)","takeaway":"A quantum information theorist resolves a 2019 open problem about how much entanglement can be distilled, and opens the paper by saying the model derived almost all of the results and techniques. He adds that validating them took 'an order of magnitude fewer' hours than it would have a year earlier.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2610.12454: On PPT entanglement distillation","url":"https://arxiv.org/abs/2610.12454","type":"paper","group":"primary","domain":"arxiv.org"}],"official":1,"filed":"2026-10-12","updated":"2026-10-12","orgs":["Scuola Normale Superiore","OpenAI"],"title":"PPT-distillable entanglement can fall strictly below the regularised Rains bound: results \"derived almost entirely by ChatGPT Astra\" (Lami)","summary":"On 8 Oct 2026 Ludovico Lami (Scuola Normale Superiore, Pisa) posted arXiv 2610.12454. It gives a regularised formula for the entanglement distillable with PPT operations and two new single-letter upper bounds, and uses them to show that the PPT distillable entanglement can be strictly smaller than the regularised Rains bound, \"resolving an open problem in the theory of entanglement manipulation\" (Regula et al., 2019). For a 3×3 Werner state a certified upper bound of 0.62107 ebits lies below the Rains value of about 0.64766. The introduction begins: \"The main results and techniques presented here have been derived almost entirely by ChatGPT Astra.\" Unrefereed preprint, checked by the author.","key_facts":["Paper: 'On PPT entanglement distillation', arXiv 2610.12454 [quant-ph], 8 Oct 2026; Ludovico Lami, Scuola Normale Superiore, Pisa (single author); 39 pages","Results (abstract): '(a) a regularised formula for the PPT distillable entanglement in terms of a measured-relative-entropy-like quantity; and (b) two different single-letter converses, one based on operator quadratic forms and the other on Hirschman's strengthening of the Hadamard three-line theorem'","Open problem resolved (abstract): 'we show that the PPT distillable entanglement can be strictly smaller than the regularised Rains bound, thereby resolving an open problem in the theory of entanglement manipulation [Regula et al., NJP 21:103017, 2019]'","Explicit gap: 3×3 Werner state with antisymmetric weight 25/26: certified upper bound 0.62107 ebits, against a (regularised) Rains bound of (25/26)·log2 5 − log2 3 ≈ 0.64766 ebits","Also: a faithful lower bound on PPT distillable entanglement in terms of the entanglement negativity, a quantitative version of the known fact that every NPT state is PPT-distillable","AI disclosure (note opening the introduction): 'The main results and techniques presented here have been derived almost entirely by ChatGPT Astra. The human author (yours truly) gave many suggestions on how to extend and generalise the initial findings, which applied only to Werner states, and spent many hours (but an order of magnitude fewer than would have been needed a year ago) validating and improving the proof techniques, as well as adapting the presentation to his style.'","The numerical separation is backed by companion certificate files (appendices on certified parameters and quadrature)"],"key_numbers":[],"tags":["physics","quantum-information","entanglement-distillation","rains-bound","werner-states","gpt-6-astra","ai-generated-proof"],"science":{"field":"physics","subfield":"quantum information theory","problem":"Is the regularised Rains bound always equal to the entanglement distillable under PPT operations? (open problem of Regula et al., 2019)","result":"No: the PPT distillable entanglement can be strictly smaller, already for 3×3 Werner states (≤ 0.62107 vs ≈ 0.64766 ebits); plus a regularised formula and two single-letter converse bounds.","open_since":"2019","ai_system":["GPT-6 Astra"],"human_role":"AI-derived per the author ('derived almost entirely by ChatGPT Astra'); the author suggested generalisations beyond Werner states, validated and improved the proofs and rewrote the presentation","verification":{"key":"preprint","label":"Preprint only","text":"Unrefereed preprint; proofs validated by the author, numerical gap supported by certificate files"},"status":"pending","shock":"A specialist states on the first page that the model, not he, derived the results.","short":"PPT entanglement distillation vs the Rains bound"},"body_md":"## What happened\n\nEntanglement distillation turns many copies of a noisy entangled state into fewer, nearly perfect entangled pairs (\"ebits\"). The\nbest achievable rate with local operations is very hard to compute, so theorists study a larger, more tractable class of\noperations, the PPT channels, and upper bounds such as the Rains bound. Whether the regularised Rains bound is always attained by\nPPT operations was listed as an open problem in 2019.\n\nLami's paper answers no. It gives a formula for the PPT distillable entanglement, derives two new upper bounds, and exhibits a\nsimple family of states (Werner states on two three-level systems) where the new bound is provably below the Rains bound.\n\nThe paper's first note attributes the work to the model, named there as \"ChatGPT Astra\" (OpenAI's GPT-6 Astra). The author\ndescribes his own part as suggesting generalisations, spending many hours on validation, and adapting the text to his style.\n\n## Why it matters\n\nThe disclosure is unusually direct for a single-author theory paper. His\nremark about time is a data point on how fast the checking burden is changing: validation took an order of magnitude less time\nthan it would have a year before, by his estimate.","disputed":[{"label":"Verification","text":"Unrefereed preprint; proofs validated by the author, numerical gap supported by certificate files","sources":[]}],"related":[{"id":"2026-10-09-kinetic-krylov-safonov-pucci-conjecture-gpt-6-astra","url":"https://postcutoff.com/e/2026-10-09-kinetic-krylov-safonov-pucci-conjecture-gpt-6-astra/","date":"2026-10-09","date_precision":"day","short_title":"\"We need ABP\": six PDE specialists publish GPT-6 Astra's proofs of the kinetic Krylov–Safonov theorem and of Pucci's 1966 conjecture, with full chats (Loher, Mooney, Mouhot, Niebel, Silvestre, Zhu)","deck":null,"takeaway":"Six analysts, among them Clément Mouhot and Luis Silvestre, say the missing estimate behind a long-open regularity theorem for kinetic equations was found by GPT-6 Astra Ultra on 6 Sept 2026 with no human contribution. They wrote a human exposition and published the prompts, chats and AI manuscripts, and state that they claim no credit.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":5,"official":5,"filed":"2026-10-12","updated":"2026-10-12","orgs":["OpenAI","University of Cambridge","University of Chicago","UC Irvine"]},{"id":"2026-10-09-random-permutations-universal-alon-gpt-6-pro","url":"https://postcutoff.com/e/2026-10-09-random-permutations-universal-alon-gpt-6-pro/","date":"2026-10-09","date_precision":"day","short_title":"Random permutations of quadratic length contain every pattern","deck":"Alon's 1000n² problem solved, 'the proof was found by GPT-6 Pro' (Chen, Wang)","takeaway":"The authors of this combinatorics paper state in the abstract that the model found the proof and that they 'do not claim credit for the proof ideas'. It settles the order of magnitude in a problem posed by Noga Alon.","category":"science","category_label":"Science & math","importance":3,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-12","updated":"2026-10-12","orgs":["Beijing Institute of Technology","OpenAI"]},{"id":"2026-09-30-ai-assisted-conjecture-wave-summer-2026","url":"https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/","date":"2026-09-30","date_precision":"day","short_title":"Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help","deck":null,"takeaway":"This entry catalogues about 50 of them, with the AI role as the authors state it.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":9,"official":4,"filed":"2026-09-30","updated":"2026-10-12","orgs":["OpenAI","Anthropic","Google DeepMind","various mathematicians"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-12","type":"filed","text":"Created from the arXiv PDF (found by a manual arXiv scan)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-12","run":null,"sources_read":"The arXiv PDF (found by a manual arXiv scan)","updated":"2026-10-12","human_review":null,"version":null},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":161,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":100,"in_training_data":false},{"model_id":"gemini-3-8-flash","name":"Gemini 3.8 Flash","cutoff":"2026-03","days_after":191,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":130,"in_training_data":false}],"short_url":null}