The absolutely maximally entangled (AME) state is a concept in quantum information science, which has many applications in quantum error-correcting code,[1] discrete AdS/CFT correspondence,[2] AdS/CMT correspondence,[2] and more.
It is the multipartite generalization of the bipartite maximally entangled state.
The bipartite maximally entangled state
is the one for which the reduced density operators are maximally mixed, i.e.,
is called absolutely maximally entangled if for any bipartition
, the reduced density operator is maximally mixed
There is a list of AME states in low dimensions created by Huber and Wyderka.
[3][4] The existence of the AME state can be transformed into the existence of the solution for a specific quantum marginal problem.
[5] The AME can also be used to build a kind of quantum error-correcting code called holographic error-correcting code.