[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85040-en":3,"doc-seo-85040-105":29,"detail-sidebar-cat-0-en-105":91},{"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":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},85040,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",8,"Research & Report","Smoothing Exponents and Decoupling in Semifinite von Neumann Algebras","Study of the smoothing exponent of the max-relative entropy in semifinite von Neumann algebras. An exact exponent formula is established, with operator-algebraic replacements replacing dimension-dependent tools from finite-dimensional proofs. The smoothing behavior is shown to be determined by the intrinsic structure of the von Neumann algebra rather than matrix dimension estimates. As an application, catalytic quantum information decoupling is formulated with a semifinite von Neumann algebraic reference system and a layer-cake lemma yields a matching semifinite reliability exponent.","arXiv :2607 .07997v 1 [ cs .IT] 9 Jul 2026  \nSMOOTHING EXPONENTS AND DECOUPLING IN SEMIFINITE VON NEUMANN ALGEBRAS  \nZHIWEN LIN, HONGSEN QIU, AND XINYU ZHANG  \nAbstract. We study the smoothing exponent of the max-relative entropy in semifinite von Neumann algebras. Our main result gives an exact exponent formula in this setting. The proof develops operatoralgebraic replacements for the dimension-dependent tools used in finitedimensional arguments. These ingredients show that the smoothing exponent is governed by the underlying von Neumann algebraic structure rather than by matrix dimension estimates.  \nAs an application, we formulate catalytic quantum information decoupling with a semifinite von Neumann algebraic reference system. We prove an intrinsic layer-cake lemma for von Neumann algebras, which removes the countable spectrum assumption in the finite-dimensional proof and yields the corresponding semifinite estimate. Consequently, the decoupling reliability exponent is described by the same sandwiched Rényi mutual information formula as in the finite-dimensional theory.  \n1. Introduction  \nA natural framework for going beyond finite-dimensional quantum systems is provided by von Neumann algebras. This point of view has already become a useful language in quantum information theory. Rényi relative entropies and sandwiched Rényi quantities have been formulated in this setting, e.g [10, 11] .  \nMore recently, this operator-algebraic viewpoint has been connected with asymptotic information theory. Fawzi, Gao and Rahaman established asymptotic equipartition theorems for smooth entropies in von Neumann algebras [8], showing that smooth entropy theory admits a genuine von Neumann algebraic formulation. In a related direction, Junge and Laracuente studied strong converse exponents for asymptotic hypothesis testing in type-III von Neumann algebras [12] . These results indicate that the operational theory of quantum information is not merely a finite-dimensional phenomenon.  \nThis perspective is particularly relevant for semifinite von Neumann algebras. However, the standard finite-dimensional arguments based on spectral pinching, eigenvalue counting and so on, can not be transferred directly. One must instead use tools intrinsic to the semifinite algebra.  \nThe goal of the present paper is to develop this intrinsic approach for the smoothing exponent of the max-relative entropy. The finite-dimensional exponent formula of Li, Yao and Hayashi [15] is a sharp result in large deviations, and it is closely related to privacy amplification and to the exponential  \n2 ZHIWEN LIN, HONGSEN QIU, AND XINYU ZHANG  \nbehavior of smooth entropies. We prove that the same exponent formula persists in the semifinite setting. The proof replaces dimension-dependent ingredients by operator-algebraic ones.  \nThis also leads to an operator-algebraic form of catalytic decoupling. Infinite dimensions, Li and Yao characterized the reliability function of quantum information decoupling in terms of the sandwiched Rényi mutual information [14] . In the present paper, we allow the reference system to bea semifinite von Neumann algebra. Our decoupling result shows that the same reliability formula survives in this broader setting. In this sense, the decoupling exponent is governed by the von Neumann algebraic structure of the bipartite normal state.  \nThis operator-algebraic viewpoint is also a natural structural language for quantum information beyond matrix algebras. Von Neumann algebras were originally developed with quantum theory as one of their main motivations, and their role in quantum physics has remained central through algebraic quantum field theory, subfactor theory, and modular theory [16] .  \nThese developments show that operator algebras provide a natural framework for quantum information whenever the reference system is not adequately described by matrices.  \n2. Preliminaries  \n2.1. Semifinite von Neumann algebras and noncommutative Lpspaces. We ","cbCaikkFT9Ulip3W","https://ap.wps.com/l/cbCaikkFT9Ulip3W","pdf",298595,1,51,"English","en",105,"# Introduction\n# Preliminaries\n## Semifinite von Neumann algebras and noncommutative Lp-spaces","[{\"question\":\"What is the main problem addressed by the paper?\",\"answer\":\"The paper studies the smoothing exponent of the max-relative entropy in semifinite von Neumann algebras and derives an exact exponent formula.\"},{\"question\":\"How does the proof differ from finite-dimensional approaches?\",\"answer\":\"It replaces dimension-dependent tools used in finite-dimensional arguments with operator-algebraic ingredients intrinsic to semifinite von Neumann algebras.\"},{\"question\":\"What is the application to quantum information decoupling?\",\"answer\":\"The authors formulate catalytic quantum decoupling with a semifinite von Neumann algebraic reference system, prove an intrinsic layer-cake lemma, and express the decoupling reliability exponent using the same sandwiched Rényi mutual information formula as in finite-dimensional 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is the main problem addressed by the paper?","Question",{"text":75,"@type":76},"The paper studies the smoothing exponent of the max-relative entropy in semifinite von Neumann algebras and derives an exact exponent formula.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proof differ from finite-dimensional approaches?",{"text":80,"@type":76},"It replaces dimension-dependent tools used in finite-dimensional arguments with operator-algebraic ingredients intrinsic to semifinite von Neumann algebras.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the application to quantum information decoupling?",{"text":84,"@type":76},"The authors formulate catalytic quantum decoupling with a semifinite von Neumann algebraic reference system, prove an intrinsic layer-cake lemma, and express the decoupling reliability exponent using the same sandwiched Rényi mutual information formula as in finite-dimensional 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