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Meanwhile, quantum information about the system becomes inaccessible to local observers. Here we prove a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>O<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-sized region we call the \"quantum Markov blanket,\" any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of  Brand\u00e3o et al. (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext class=\"MJX-tex-mathit\" mathvariant=\"italic\">Nat. comm. 6:7908<\/mml:mtext><\/mml:mrow><\/mml:math>) in which the excluded region was allowed to grow with total environment size. It may also be seen as a new consequence of the principles of no-cloning or monogamy of entanglement. Our proof offers a constructive optimization procedure for determining the \"quantum Markov blanket\" region, as well as the effective measurement induced by the evolution. Alternatively, under channel-state duality, our result characterizes the marginals of multipartite states.<\/jats:p>","DOI":"10.22331\/q-2021-09-28-555","type":"journal-article","created":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T16:13:10Z","timestamp":1632845590000},"page":"555","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":14,"title":["Emergent classicality in general multipartite states and channels"],"prefix":"10.22331","volume":"5","author":[{"given":"Xiao-Liang","family":"Qi","sequence":"first","affiliation":[{"name":"Department of Physics, Stanford University, Stanford, CA 94305-4060, USA"}]},{"given":"Daniel","family":"Ranard","sequence":"additional","affiliation":[{"name":"Department of Physics, Stanford University, Stanford, CA 94305-4060, USA"}]}],"member":"9598","published-online":{"date-parts":[[2021,9,28]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Harold Ollivier, David Poulin, and Wojciech H Zurek. 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