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The operationally noncontextual ontological model coincides with standard Spekkens noncontextual ontological models for tomographically complete scenarios, while covering the non-tomographically complete case with a new notion of a reduced space, which we motivate following the guiding principles of noncontextuality. A mathematical criterion, called unit separability<\/mml:mtext><\/mml:mrow><\/mml:math>, is formulated as the relevant classicality criterion \u2013 the name is inspired by the usual notion of quantum state separability. Using this criterion, we derive a new upper bound on the cardinality of the ontic space. Then, we recast the unit separability criterion as a (possibly infinite) set of linear constraints, from which we obtain two separate hierarchies of algorithmic tests to witness the non-classicality or certify the classicality of a scenario. Finally, we reformulate our results in the framework of generalized probabilistic theories and discuss the implications for simplex-embeddability in such theories.<\/jats:p>","DOI":"10.22331\/q-2022-06-07-732","type":"journal-article","created":{"date-parts":[[2022,6,7]],"date-time":"2022-06-07T16:40:52Z","timestamp":1654620052000},"page":"732","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":13,"title":["Solvable Criterion for the Contextuality of any Prepare-and-Measure Scenario"],"prefix":"10.22331","volume":"6","author":[{"given":"Victor","family":"Gitton","sequence":"first","affiliation":[{"name":"Institute for Theoretical Physics, ETH Z\u00fcrich, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mischa P.","family":"Woods","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, ETH Z\u00fcrich, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,6,7]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. 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