We present new bounds on the existence of quantum maximum distance separable
\ncodes (QMDS): the length n of all non-trivial QMDS codes with local dimension
\nD and distance d is bounded by n \u2264 D^2 + d \u2212 2. We obtain their weight
\ndistribution by investigating families of QMDS codes, and present additional
\nbounds that arise from Rains\u2019 shadow inequalities. Our main result can be seen
\nas a generalization of bounds that are known for the two special cases of
\nstabilizer QMDS codes and absolutely maximally entangled states, and confirms
\nthe quantum MDS conjecture in the special case of distance-three codes.
\nBecause the existence of QMDS codes is directly linked to that of highly
\nentangled subspaces (in which every vector has uniform r-body marginals) of
\nmaximal dimension, our methods directly carry over to address questions in
\nmultipartite entanglement.<\/p>\n","protected":false},"excerpt":{"rendered":"
We present new bounds on the existence of quantum maximum distance separable codes (QMDS): the length n of all non-trivial QMDS codes with local dimension D and distance d is bounded by n \u2264 D^2 + d \u2212 2. We obtain their weight distribution by investigating families of QMDS codes, and present additional bounds that […]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1152","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1152","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/20"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=1152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}