{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/one-half-reflected-entropy-is-not-a-lower","title":"One-half reflected entropy is not a lower bound for entanglement of purification","arxiv_id":"2309.02506","date":"2023-09-05","proceeding":null,"authors":["Josiah Couch","Phuc Nguyen","Sarah Racz","Georgios Stratis","Yuxuan Zhang"],"abstract":"In recent work, Akers et al. proved that the entanglement of purification $E_p(A:B)$ is bounded below by half of the $q$-R\\'enyi reflected entropy $S_R^{(q)}(A:B)$ for all $q\\geq2$, showing that $E_p(A:B) = \\frac{1}{2} S_R^{(q)}(A:B)$ for a class of random tensor network states. Naturally, the authors raise the question of whether a similar bound holds at $q = 1$. Our work answers that question in the negative by finding explicit counter-examples, which we arrive at through numerical optimization. Nevertheless, this result does not preclude the possibility that restricted sets of states, such as CFT states with semi-classical gravity duals, could obey the bound in question.","url_abs":"https://arxiv.org/abs/2309.02506v2","url_pdf":"https://arxiv.org/pdf/2309.02506v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"one-half-reflected-entropy-is-not-a-lower","repo_url":"https://github.com/iosialectus/eofp_minus_half_re_opt","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}