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While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.<\/jats:p>","DOI":"10.22331\/q-2022-01-11-621","type":"journal-article","created":{"date-parts":[[2022,1,11]],"date-time":"2022-01-11T13:31:06Z","timestamp":1641907866000},"page":"621","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":40,"title":["Experimental entanglement of temporal order"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4249-522X","authenticated-orcid":false,"given":"Giulia","family":"Rubino","sequence":"first","affiliation":[{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria"},{"name":"Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical & Electronic Engineering, University of Bristol, Bristol BS8 1FD, United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lee A.","family":"Rozema","sequence":"additional","affiliation":[{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Massa","sequence":"additional","affiliation":[{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mateus","family":"Ara\u00fajo","sequence":"additional","affiliation":[{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria"},{"name":"Institute for Quantum Optics & Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Magdalena","family":"Zych","sequence":"additional","affiliation":[{"name":"Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"\u010caslav","family":"Brukner","sequence":"additional","affiliation":[{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria"},{"name":"Institute for Quantum Optics & Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4249-522X","authenticated-orcid":false,"given":"Philip","family":"Walther","sequence":"additional","affiliation":[{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2022,1,11]]},"reference":[{"key":"0","unstructured":"We test hypothesis IIb by placing the two operations individually in a single quantum switch, and we show that each operation is local. 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