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The resource for generating such sequences is the internal dimension, or <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>m<\/mml:mi><mml:mi>e<\/mml:mi><mml:mi>m<\/mml:mi><mml:mi>o<\/mml:mi><mml:mi>r<\/mml:mi><mml:mi>y<\/mml:mi><\/mml:math>, of the system. We characterize the minimum memory requirements for sequences to be obtained deterministically, and numerically investigate the probabilistic behavior below this memory threshold, in both classical and quantum scenarios. A particular class of sequences is found to offer an upper-bound for all other sequences, which suggests a nontrivial universal upper-bound of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>1<\/mml:mn><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mo>\/<\/mml:mo><\/mml:mrow><mml:mi>e<\/mml:mi><\/mml:math> for the classical probability of realization of any sequence below this memory threshold. We further present evidence that no such nontrivial bound exists in the quantum case.<\/jats:p>","DOI":"10.22331\/q-2022-01-18-623","type":"journal-article","created":{"date-parts":[[2022,1,18]],"date-time":"2022-01-18T11:52:09Z","timestamp":1642506729000},"page":"623","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":14,"title":["Temporal correlations in the simplest measurement sequences"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6530-8271","authenticated-orcid":false,"given":"Lucas B.","family":"Vieira","sequence":"first","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6562-7862","authenticated-orcid":false,"given":"Costantino","family":"Budroni","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"},{"name":"Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,1,18]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"M. 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