[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85581-en":3,"doc-seo-85581-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"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},85581,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","The Power of Unentanglement Without Destructive Interference","Stoquasticity, which arises in physical systems without the sign problem and without destructive interference from sign cancellations, motivates StoqMA, a quantum-inspired intermediate class between MA and AM. Unentanglement likewise leads to QMA(2), extending QMA to two unentangled proofs. This work systematically studies unentanglement power without destructive interference via StoqMA(2), a class of unentangled stoquastic Merlin–Arthur proof systems, connecting complexity bounds to non-negative tensor optimization and tightening parameters under ETH.","arXiv :2604 .27886v2 [ quant-ph] 12 Jul 2026  \nThe power of unentanglement without destructive interference  \nYupan Liu∗1 and Pei Wu†2  \n1 School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne  \n2 Department of Computer Science and Engineering, The Pennsylvania State University  \nAbstract  \nStoquasticity, originating in physical systems free of the so-called sign problem and avoiding destructive interference from sign cancellations, gives rise to StoqMA, introduced by Bravyi, Bessen, and Terhal (2006), a quantum-inspired intermediate class between MA and AM. Unentanglement similarly gives rise to QMA(2), introduced by Kobayashi, Matsumoto, and Yamakami (CJTCS 2009), which generalizes QMA to two unentangled proofs and still has only the trivial NEXP upper bound.  \nIn this work, we initiate a systematic study of the power of unentanglement without destructive interference via StoqMA(2), the class of unentangled stoquastic Merlin–Arthur proof systems. Beyond its complexity-theoretic interest, StoqMA(2) is closely connected to the optimality of non-negative tensor optimization algorithms. We highlight:  \n1. NPlelin⊆ Stog theqMAbest(2k)nwowithn M(√An(2)-)qluobitwerproofsboundasnd comexceptplfeteornpeesrs error 2−pfect compleotlyloenges(ns) , pMaeraanl--  \nwhile, the Sum-of-Squares algorithm of Barak, Kelner, and Steurer (STOC 2014) gives an exponential-time upper bound for StoqMA(2) . Our tightened analysis shows the essential optimality of the parameters in both our protocol and the BKS algorithm under the Exponential-Time Hypothesis (ETH) .  \n2. Under nearly perfect completeness, StoqMA(2) admits sharper deterministic upper bounds: for StoqMA(2)1 , the parameter dependence in the general ETH-optimal time bound can be exponentially improved, or the bound achieved simultaneously with polynomial space.  \n3. For logarithmic-size proofs, NP ⊆ StoqMA(2)log with completeness error O (n−2) and implicitly vanishing gap. Meanwhile, StoqMA(2)log ⊆ MA, and consequently quantuminspired randomness enables exponentially shorter unentangled proofs even under the standard derandomization assumption MA = NP.  \n4. PreciseStoqMA(2), a variant of StoqMA(2) with exponentially small promise gap, cannot achieve perfect completeness unless EXP = NEXP. In contrast, PreciseStoqMA achieves perfect completeness, since PSPACE ⊆ PreciseStoqMA 1 .  \nOur lower bounds are obtained by stoquastizing the short-proof QMA(2) protocols using distribution testing techniques. Our upper bounds for the nearly perfect completeness case are proved via our rectangular closure testing framework, a new combinatorial technique tailored to StoqMA(2)1 .  \n∗ Email: [yupan](yupan.liu@epfl.ch)[.](yupan.liu@epfl.ch)[liu@epfl](yupan.liu@epfl.ch)[.](yupan.liu@epfl.ch)[ch](yupan.liu@epfl.ch)[ ](yupan.liu@epfl.ch)†Email: [pei](pei.wu@psu.edu)[.](pei.wu@psu.edu)[wu@psu](pei.wu@psu.edu)[.](pei.wu@psu.edu)[edu](pei.wu@psu.edu)  \nContents  \n1 Introduction 1  \n1.1 Main results ....................................... 4  \n1.2 Proof techniques .................................... 6  \n1.3 Discussion and open problems ............................. 11  \n1.4 Related work ...................................... 11  \n2 Preliminaries 12  \n2.1 Information-theoretic measures ............................ 13  \n2.2 (Stoquastic) separable values of square Hermitian matrices ............. 14  \n2.3 Stoquastic algorithmic toolkit ............................. 15  \n3 Parallel repetition in stoquastic Merlin–Arthur proof systems 15  \n3.1 The multiplicativity of the stoquastic separable values ............... 18  \n3.2 Two StoqMA (k )-complete problems from the class definition ............ 20  \n3.2.1 Separable Stoquastic Close Image to Uniform ................ 20  \n3.2.2 Separable Reversible Circuit Distinguishability ............... 21  \n3.3 StoqMA (k ) is closed under direct product ...................... 22  \n4 Robustness of StoqMA(2) 23  \n4.1 StoqMA (k ) vs. StoqMA(2) ..........","cbCaiabuf1iEPmHB","https://ap.wps.com/l/cbCaiabuf1iEPmHB","pdf",1309695,1,84,"English","en",105,"# Introduction\n## Main results\n## Proof techniques\n## Discussion and open problems\n## Related work\n# Preliminaries\n## Information-theoretic measures\n## Stoquastic separable values of square Hermitian matrices\n## Stoquastic algorithmic toolkit\n# Parallel repetition in stoquastic Merlin–Arthur proof systems\n## The multiplicativity of the stoquastic separable values\n## Two StoqMA (k )-complete problems from the class definition\n## StoqMA (k ) is closed under direct product\n# Robustness of StoqMA(2)\n## StoqMA (k ) vs. StoqMA(2)\n## SymStoqMA (k ) vs. StoqMA (k )\n# The power of StoqMA(2) via distribution testing\n## A SymStoqMA ( √n) protocol for (1,η)-GapCG\n## A StoqMA log(2) protocol with inverse-polynomial gap\n# Upper bounds for StoqMA (k ) with logarithmic-size proofs\n## StoqMAlog ⊆ BPP and general rETH-optimal BPTIME upper bound\n## StoqMA (k )log ⊆ MA\n# Upper bounds for StoqMA (k ) with nearly perfect completeness\n## Rectangular structure of non-negative product states\n## Rectangular closure testing and its consequences\n# A deterministic exponential-time upper bound for StoqMA (k )\n## PSPACE ⊆ PreciseStoqMA 1","[{\"question\":\"What relationship does the paper establish between stoquasticity, StoqMA, and unentanglement-based proof classes?\",\"answer\":\"It explains that stoquasticity motivates StoqMA as a quantum-inspired class between MA and AM. It then describes how unentanglement leads to QMA(2) and focuses on the unentangled stoquastic Merlin–Arthur class StoqMA(2).\"},{\"question\":\"What is the key complexity-theoretic goal of studying StoqMA(2) in this work?\",\"answer\":\"The work investigates the power of unentanglement without destructive interference by deriving lower and upper bounds for StoqMA(2) under different completeness and proof-length regimes, and by tightening parameter dependences using ETH.\"},{\"question\":\"How do the paper’s upper bounds differ between nearly perfect completeness and logarithmic-size proofs?\",\"answer\":\"For nearly perfect completeness, the paper proves sharper deterministic upper bounds via rectangular closure testing, improving parameter dependence under ETH. For logarithmic-size proofs, it shows inclusions such as StoqMA(2)log ⊆ MA and implications tied to derandomization assumptions (e.g., MA = NP) for shorter unentangled proofs.\"}]",1784204729,212,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"the-power-of-unentanglement-without-destructive-interference","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/the-power-of-unentanglement-without-destructive-interference/85581/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What relationship does the paper establish between stoquasticity, StoqMA, and unentanglement-based proof classes?","Question",{"text":74,"@type":75},"It explains that stoquasticity motivates StoqMA as a quantum-inspired class between MA and AM. It then describes how unentanglement leads to QMA(2) and focuses on the unentangled stoquastic Merlin–Arthur class StoqMA(2).","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What is the key complexity-theoretic goal of studying StoqMA(2) in this work?",{"text":79,"@type":75},"The work investigates the power of unentanglement without destructive interference by deriving lower and upper bounds for StoqMA(2) under different completeness and proof-length regimes, and by tightening parameter dependences using ETH.",{"name":81,"@type":72,"acceptedAnswer":82},"How do the paper’s upper bounds differ between nearly perfect completeness and logarithmic-size proofs?",{"text":83,"@type":75},"For nearly perfect completeness, the paper proves sharper deterministic upper bounds via rectangular closure testing, improving parameter dependence under ETH. For logarithmic-size proofs, it shows inclusions such as StoqMA(2)log ⊆ MA and implications tied to derandomization assumptions (e.g., MA = NP) for shorter unentangled proofs.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]