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However, this bound cannot be saturated by either classical machines or their enhanced quantum counterparts. Simulating a process fundamentally requires us to store more information in the present than is shared between the past and the future. Here, we consider a generalization of hidden Markov models beyond classical and quantum models, referred to as n-machines, that allow for negative quasiprobabilities. We show that under the collision entropy measure of information, the minimal memory of such models can equal the excess entropy. Our results suggest that negativity can be a useful resource for achieving nonclassical memory advantage.<\/jats:p>","DOI":"10.22331\/q-2026-02-23-2005","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T12:32:51Z","timestamp":1771849971000},"page":"2005","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Ideal stochastic process modeling with post-quantum quasiprobabilistic theories"],"prefix":"10.22331","volume":"10","author":[{"given":"Kelvin","family":"Onggadinata","sequence":"first","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore"},{"name":"Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew","family":"Tanggara","sequence":"additional","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore"},{"name":"Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mile","family":"Gu","sequence":"additional","affiliation":[{"name":"Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore."},{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore"},{"name":"Centre for Quantum Technologies, Nanyang Technological University, Singapore 637371, Singapore"},{"name":"Majulab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI No. 3654, Singapore 117543, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dagomir","family":"Kaszlikowski","sequence":"additional","affiliation":[{"name":"Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore"},{"name":"Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,2,23]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"L. 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