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But what are the essential physical principles of quantum theory that make this mechanism possible? We address this question by formulating the simplest instance of Darwinism \u2013 CNOT-like <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>f<\/mml:mi><mml:mi>a<\/mml:mi><mml:mi>n<\/mml:mi><\/mml:math>-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>o<\/mml:mi><mml:mi>u<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:math> interactions \u2013 in a class of probabilistic theories that contain classical and quantum theory as special cases. We determine necessary and sufficient conditions for any theory to admit such interactions. We find that every theory with non-classical features that admits this idealized spreading of classical information must have both entangled states and entangled measurements. Furthermore, we show that Spekkens' toy theory admits this form of Darwinism, and so do all probabilistic theories that satisfy principles like strong symmetry, or contain a certain type of decoherence processes. Our result suggests the counter-intuitive general principle that in the presence of local non-classicality, a classical world can only emerge if this non-classicality can be \"amplified\" to a form of entanglement.<\/jats:p>","DOI":"10.22331\/q-2022-01-31-636","type":"journal-article","created":{"date-parts":[[2022,1,31]],"date-time":"2022-01-31T13:34:50Z","timestamp":1643636090000},"page":"636","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Quantum Darwinism and the spreading of classical information in non-classical theories"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4248-2015","authenticated-orcid":false,"given":"Roberto D.","family":"Baldijao","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica Gleb Wataghin, Universidade Estadual de Campinas, Campinas, SP 13083-859, Brazil"},{"name":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria"}]},{"given":"Marius","family":"Krumm","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria"},{"name":"Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3747-9997","authenticated-orcid":false,"given":"Andrew J. P.","family":"Garner","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8086-5586","authenticated-orcid":false,"given":"Markus P.","family":"Mueller","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria"},{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria"},{"name":"Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada"}]}],"member":"9598","published-online":{"date-parts":[[2022,1,31]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"W. H. Zurek. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. 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