{"id":197712,"date":"2024-10-14T21:25:58","date_gmt":"2024-10-15T02:25:58","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2024\/10\/quantum-teleportation-implies-symmetry-protected-topological-order"},"modified":"2024-10-14T21:25:58","modified_gmt":"2024-10-15T02:25:58","slug":"quantum-teleportation-implies-symmetry-protected-topological-order","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2024\/10\/quantum-teleportation-implies-symmetry-protected-topological-order","title":{"rendered":"Quantum teleportation implies symmetry-protected topological order"},"content":{"rendered":"<p style=\"padding-right: 20px\"><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/quantum-teleportation-implies-symmetry-protected-topological-order3.jpg\"><\/a><\/p>\n<p>Now in Quantum: by Yifan Hong, David T. Stephen, and Aaron J. Friedman <a href=\"https:\/\/doi.org\/10.22331\/q-2024-10-10-1499\">https:\/\/doi.org\/10.22331\/q-2024-10-10-1499<\/a><\/p>\n<hr>\n<p>Yifan Hong, David T. Stephen, and Aaron J. Friedman, Quantum 8, 1499 (2024). We constrain a broad class of teleportation protocols using insights from locality. In the \u201cstandard\u201d teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a \u201cresource state\u201d exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry $\\mathcal{G}_{k}= (\\mathbb{Z}_2 \\times \\mathbb{Z}_2)^k$. The $k$ logical states are teleported between the edges of the chain by measuring the corresponding $2k$ string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of $k$ qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Now in Quantum: by Yifan Hong, David T. Stephen, and Aaron J. Friedman https:\/\/doi.org\/10.22331\/q-2024-10-10-1499 Yifan Hong, David T. Stephen, and Aaron J. Friedman, Quantum 8, 1499 (2024). We constrain a broad class of teleportation protocols using insights from locality. In the \u201cstandard\u201d teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear [\u2026]<\/p>\n","protected":false},"author":662,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1617],"tags":[],"class_list":["post-197712","post","type-post","status-publish","format-standard","hentry","category-quantum-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/197712","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/662"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=197712"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/197712\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=197712"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=197712"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=197712"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}