{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T03:08:59Z","timestamp":1761102539028,"version":"3.32.0"},"reference-count":33,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T00:00:00Z","timestamp":1736294400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009566","name":"Foundational Questions Institute","doi-asserted-by":"crossref","award":["FQXi-RFP-1807"],"award-info":[{"award-number":["FQXi-RFP-1807"]}],"id":[{"id":"10.13039\/100009566","id-type":"DOI","asserted-by":"crossref"}]},{"name":"ARC Future Fellowship","award":["FT180100317"],"award-info":[{"award-number":["FT180100317"]}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"crossref","award":["FA9550-21-1-0002"],"award-info":[{"award-number":["FA9550-21-1-0002"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Linear constraint systems (LCS) have proven to be a surprisingly prolific tool in the study of non-classical correlations and various related issues in quantum foundations. Many results are known for the Boolean case, yet the generalisation to systems of odd dimension is largely open. In particular, it is not known whether there exist LCS in odd dimension, which admit finite-dimensional quantum, but no classical solutions. In recent work, \\cite{QassimWallman2020} have shown that unlike in the Boolean case, where the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>n<\/mml:mi><\/mml:math>-qubit Pauli group gives rise to quantum solutions of LCS such as the Mermin-Peres square, the n-qudit Pauli group never gives rise to quantum solutions of a LCS in odd dimension. Here, we generalise this result towards the Clifford hierarchy. More precisely, we consider tensor products of groups generated by (single-qudit) Pauli and diagonal Clifford operators.<\/jats:p>","DOI":"10.22331\/q-2025-01-08-1583","type":"journal-article","created":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T17:20:02Z","timestamp":1736356802000},"page":"1583","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords"],"prefix":"10.22331","volume":"9","author":[{"given":"Markus","family":"Frembs","sequence":"first","affiliation":[{"name":"Centre for Quantum Dynamics, Griffith University, Yugambeh Country, Gold Coast, QLD 4222, Australia"}]},{"given":"Cihan","family":"Okay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bilkent University, Ankara, Turkey"}]},{"given":"Ho Yiu","family":"Chung","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bilkent University, Ankara, Turkey"}]}],"member":"9598","published-online":{"date-parts":[[2025,1,8]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Scott Aaronson and Daniel Gottesman. 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