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We identify a set of physical conditions imposed on the system dynamics, that when satisfied, lead to the aforementioned trajectory interpretation of the measurement results. We then show that when another quantum system is coupled to the observable, the operator representing it can be replaced by external noise. Crucially, the realizations of this surrogate (classical) stochastic process follow the same trajectories as those measured by the observer. Therefore, it can be said that the trajectory interpretation suggested by the Kolmogorov consistent measurements also applies in contexts other than sequential measurements.<\/jats:p>","DOI":"10.22331\/q-2024-06-27-1390","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T14:35:55Z","timestamp":1719498955000},"page":"1390","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Objectivity of classical quantum stochastic processes"],"prefix":"10.22331","volume":"8","author":[{"given":"Piotr","family":"Sza\u0144kowski","sequence":"first","affiliation":[{"name":"Institute of Physics, Polish Academy of Sciences, al. Lotnik\u00f3w 32\/46, PL 02-668 Warsaw, Poland"}]},{"given":"\u0141ukasz","family":"Cywi\u0144ski","sequence":"additional","affiliation":[{"name":"Institute of Physics, Polish Academy of Sciences, al. 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