Absolutely Maximally Entangled States: Existence and Applications

TL;DR

This paper explores the existence, properties, and applications of absolutely maximally entangled (AME) states, demonstrating their relevance for quantum secret sharing, teleportation, and entanglement swapping in quantum information science.

Contribution

It proves the existence of AME states for any number of parties with suitable dimensions and establishes their equivalence to certain quantum secret sharing schemes.

Findings

Existence of AME states for any number of parties with appropriate dimensions

Equivalence between AME states and pure state threshold quantum secret sharing schemes

Potential applications of AME states in teleportation and entanglement swapping protocols

Abstract

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.