[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84596-en":3,"doc-seo-84596-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84596,16904993612988,"Olivia Brown","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Three-qubit nonlocality paradoxes beyond GHZ","Quantum nonlocality paradoxes, exemplified by GHZ, yield maximally sharp logical obstructions to classical probabilistic models of quantum correlations and underpin unconditional quantum advantage in information-theoretic tasks. The work classifies all three-qubit nonlocality paradoxes defined via biconditional parity proofs, including every previously known example. New structural and combinatorial tools reveal a richer landscape that breaks regularity assumptions underlying earlier constructions.","arXiv :2607 .00795v2 [ quant-ph] 7 Jul 2026  \nThree-qubit nonlocality paradoxes: beyond GHZ Nadish de Silva, Santanil Jana, and Ming Yin  \nDepartment of Mathematics, Simon Fraser University, Burnaby, BC, Canada  \nQuantum nonlocality paradoxes, such as that of GHZ, provide maximally sharp logical obstructions to classical probabilistic models of quantum correlations. They are key resources in a broad variety of information-theoretic tasks that exhibit unconditional quantum advantage. For example, in nonlocal games, which are communication tasks that serve as core technical tools in recent landmark results in quantum computational complexity theory.  \nTheir role in establishing quantum advantage motivated their study by Abramsky et al. who introduced an infinite family of three-qubit paradoxes exhibiting novel conditional structure. This was later extended by the present authors into a full classification program.  \nIn this work, we completely classify all three-qubit nonlocality paradoxes established via a biconditional parity proof ; this is a very large class of paradoxes that encompasses all earlier-known examples. We do this by introducing a suite of new structural and combinatorial techniques. We find that the landscape of nonlocality paradoxes is far richer than previously understood, violating regularity conditions underlying all prior constructions.  \n1 Introduction  \nA central organising thrust of quantum computer science is to understand and exploit uniquely quantum resources towards provable advantages over classical information processing. A key role in this program is played by nonlocality [8 , 9], a property of correlations that obstructs simulation by classical probabilistic models. Nonlocality can be precisely certificated in terms of games, which serve as core technical tools in quantum information and complexity theory. As structurally clarified by Abramsky–Brandenburger [1], nonlocality (and its generalisation, contextuality) are essentially logical in character. This work addresses the problem of classifying logical proofs of nonlocality under minimal assumptions.  \nWhereas standard witnesses of nonlocality take the form of probabilistic inequalities satisfied by classical correlations but violable by quantum correlations [13], the maximal form of strong nonlocality is witnessed by a logical paradox. Nonlocality paradoxes arise from restricted joint measurability: quantum theory allows only compatible sets of measurements, called contexts, to be jointly measurable. The canonical example is due to Greenberger–Horne–Zeilinger (GHZ) [20 , 21] . They gave a three-qubit state with two measurements per qubit such that: the set of constraints describing the associated possibilistic empirical data, one for each context (i.e. a choice of one measurement on each qubit), is unsatisfiable.  \nNadish de Silva: [ndesilva@sfu.ca](ndesilva@sfu.ca)  \nSantanil Jana: [santanil_jana@sfu.ca](santanil_jana@sfu.ca)  \nMing Yin: [ming_yin_2@sfu.ca](ming_yin_2@sfu.ca)  \nParadoxes undergird probabilistic nonlocality in that all nonlocal correlations are dilutions of paradoxes by classical randomness. The nonlocal fraction [7 , 18] measures nonlocality by quantifying the degree to which correlations are paradoxical. In many information-theoretic tasks, quantum advantage scales directly with the nonlocal fraction of an available resource state. For example, nonlocal games [14] involve players—who may share a distributed resource but cannot directly communicate—giving coordinated responses to a referee’s queries. When classical correlations limit the players’ success probability, deterministic winning strategies necessarily require sharing a nonlocal paradox.  \nSuch unconditional advantages in communication tasks can be converted into rare unconditional complexity-theoretic separations. For example, Bravyi–Gosset–König [12] gave a constant-depth quantum circuit family, capable of generating and playing many nonlocal games, that cannot be ","cbCaiqWFVNUTRRz6","https://ap.wps.com/l/cbCaiqWFVNUTRRz6","pdf",837695,2,1,58,"English","en",105,"# Introduction\n## Prior work","[{\"question\":\"What problem does the paper address regarding nonlocality paradoxes?\",\"answer\":\"The paper addresses how to classify logical proofs of three-qubit nonlocality under minimal assumptions, extending the earlier classification program in the three-qubit setting.\"},{\"question\":\"How are the paradoxes characterized in this work?\",\"answer\":\"All three-qubit nonlocality paradoxes are classified via biconditional parity proofs, a large class that encompasses earlier-known examples.\"},{\"question\":\"Why are GHZ-type paradoxes important for quantum advantage?\",\"answer\":\"Nonlocality paradoxes provide strong logical obstructions that enable unconditional advantages in nonlocal games and related information-theoretic tasks, which can further support complexity-theoretic 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problem does the paper address regarding nonlocality paradoxes?","Question",{"text":75,"@type":76},"The paper addresses how to classify logical proofs of three-qubit nonlocality under minimal assumptions, extending the earlier classification program in the three-qubit setting.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are the paradoxes characterized in this work?",{"text":80,"@type":76},"All three-qubit nonlocality paradoxes are classified via biconditional parity proofs, a large class that encompasses earlier-known examples.",{"name":82,"@type":73,"acceptedAnswer":83},"Why are GHZ-type paradoxes important for quantum advantage?",{"text":84,"@type":76},"Nonlocality paradoxes provide strong logical obstructions that enable unconditional advantages in nonlocal games and related information-theoretic tasks, which can further support complexity-theoretic 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