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Here we show that it is possible to teleport a state which is also p<\/mml:mi>o<\/mml:mi>s<\/mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>-selected. Post-selection of a state &#x03A6;<\/mml:mi><\/mml:math> means that after Alice has finished her experiment she performs a measurement and only keeps runs of the experiment where the measurement outcome is &#x03A6;<\/mml:mi><\/mml:math>. We also demonstrate pre and post-selected p<\/mml:mi>o<\/mml:mi>r<\/mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>-based teleportation. Finally we use these protocols to perform instantaneous non-local quantum computation on pre and post-selected systems, and significantly reduce the entanglement required to instantaneously measure an arbitrary non-local variable of spatially separated pre and post-selected systems.<\/jats:p>","DOI":"10.22331\/q-2024-03-14-1280","type":"journal-article","created":{"date-parts":[[2024,3,14]],"date-time":"2024-03-14T10:15:12Z","timestamp":1710411312000},"page":"1280","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Teleportation of Post-Selected Quantum States"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-0365-4206","authenticated-orcid":false,"given":"Daniel","family":"Collins","sequence":"first","affiliation":[{"name":"H. H. 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