{"id":189387,"date":"2024-05-14T13:24:51","date_gmt":"2024-05-14T18:24:51","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2024\/05\/tensor-network-decompositions-for-absolutely-maximally-entangled-states"},"modified":"2024-05-14T13:24:51","modified_gmt":"2024-05-14T18:24:51","slug":"tensor-network-decompositions-for-absolutely-maximally-entangled-states","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2024\/05\/tensor-network-decompositions-for-absolutely-maximally-entangled-states","title":{"rendered":"Tensor network decompositions for absolutely maximally entangled states"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/tensor-network-decompositions-for-absolutely-maximally-entangled-states2.jpg\"><\/a><\/p>\n<p>Bal\u00e1zs Pozsgay and Ian M. Wanless, Quantum 8, 1339 (2024). Absolutely maximally entangled (AME) states of $k$ qudits (also known as perfect tensors) are quantum states that have maximal entanglement for all possible bipartitions of the sites\/parties. We consider the problem of whether such states can be decomposed into a tensor network with a small number of tensors, such that all physical and all auxiliary spaces have the same dimension $D$. We find that certain AME states with $k=6$ can be decomposed into a network with only three 4-leg tensors; we provide concrete solutions for local dimension $D=5$ and higher. Our result implies that certain AME states with six parties can be created with only three two-site unitaries from a product state of three Bell pairs, or equivalently, with six two-site unitaries acting on a product state on six qudits. We also consider the problem for $k=8$, where we find similar tensor network decompositions with six 4-leg tensors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bal\u00e1zs Pozsgay and Ian M. Wanless, Quantum 8, 1339 (2024). Absolutely maximally entangled (AME) states of $k$ qudits (also known as perfect tensors) are quantum states that have maximal entanglement for all possible bipartitions of the sites\/parties. We consider the problem of whether such states can be decomposed into a tensor network with a small [\u2026]<\/p>\n","protected":false},"author":367,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1635,1617],"tags":[],"class_list":["post-189387","post","type-post","status-publish","format-standard","hentry","category-materials","category-quantum-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/189387","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\/367"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=189387"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/189387\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=189387"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=189387"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=189387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}