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Therefore, one cannot interpret such distributions as the result of the sampling of a single trajectory. We show that, nonetheless, they do result from the sampling of one <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>p<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>i<\/mml:mi><mml:mi>r<\/mml:mi><\/mml:math> of trajectories. In this sense, rather than give up on trajectories, quantum mechanics requires to double down on them. To this purpose, we prove a generalization of the Kolmogorov extension theorem that applies to families of complex-valued bi-probability distributions (that is, defined on pairs of elements of the original sample spaces), and we employ this result in the quantum mechanical scenario. We also discuss the relation of our results with the quantum comb formalism.<\/jats:p>","DOI":"10.22331\/q-2024-08-27-1447","type":"journal-article","created":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T15:27:08Z","timestamp":1724772428000},"page":"1447","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0792-8122","authenticated-orcid":false,"given":"Davide","family":"Lonigro","sequence":"first","affiliation":[{"name":"Department Physik, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Staudtstra\u00dfe 7, 91058 Erlangen, Germany"},{"name":"Dipartimento di Matematica, Universit\u00e0 degli Studi di Bari Aldo Moro, via E. Orabona 4, 70125 Bari, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via G. Amendola 173, 70126 Bari, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8756-7904","authenticated-orcid":false,"given":"Fattah","family":"Sakuldee","sequence":"additional","affiliation":[{"name":"Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang, 200240 Shanghai, China"},{"name":"The International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, Jana Ba\u017cy\u0144skiego 1A, 80-309 Gda\u0144sk, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0162-7943","authenticated-orcid":false,"given":"\u0141ukasz","family":"Cywi\u0144ski","sequence":"additional","affiliation":[{"name":"Institute of Physics, Polish Academy of Sciences, al. 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