Absolutely Maximally Entangled States: Existence and Applications

We investigate absolutely maximally entangled (AME) states, which are multipartite quantum states that are maximally entangled with respect to any possible bipartition. These strong entanglement properties make them a powerful resource for a variety of quantum information protocols. In this paper, we show the existence of AME states for any number of parties, given that the dimension of the involved systems is chosen appropriately. We prove the equivalence of AME states shared between an even number of parties and pure state threshold quantum secret sharing (QSS) schemes, and prove necessary and sufficient entanglement properties for a wider class of ramp QSS schemes. We further show how AME states can be used as a valuable resource for open-destination teleportation protocols and to what extend entanglement swapping generalizes to AME states.