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Can we even talk about `repetitions&apos; of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary, possibly indefinite, causal structure are independent and identically distributed? Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by so-called \"de Finetti theorems\", which connect a simple and easy-to-justify condition \u2013 symmetry under exchange \u2013 with a very particular multipartite structure: a mixture of identical states\/channels. Here we extend the result to processes with arbitrary causal structure, including indefinite causal order and multi-time, non-Markovian processes applicable to noisy quantum devices. The result also implies a new class of de Finetti theorems for quantum states subject to a large class of linear constraints, which can be of independent interest.<\/jats:p>","DOI":"10.22331\/q-2025-02-11-1628","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T16:37:27Z","timestamp":1739291847000},"page":"1628","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["A de Finetti theorem for quantum causal structures"],"prefix":"10.22331","volume":"9","author":[{"given":"Fabio","family":"Costa","sequence":"first","affiliation":[{"name":"Nordita, Stockholm University and KTH Royal Institute of Technology, Hannes Alfv\u00e9ns v\u00e4g 12 Stockholm, 106 91, Sweden"},{"name":"School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia"}]},{"given":"Jonathan","family":"Barrett","sequence":"additional","affiliation":[{"name":"Quantum Group, Department of Computer Science, University of Oxford"}]},{"given":"Sally","family":"Shrapnel","sequence":"additional","affiliation":[{"name":"ARC Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia"}]}],"member":"9598","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"0","unstructured":"Franti\u0161ek Barto\u0161, Alexandra Sarafoglou, Henrik R. 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