Absolutely Maximally Entangled Qudit Graph States

TL;DR

This paper explores the representation of absolutely maximally entangled (AME) states using graph states, demonstrating their existence for all parties and their application in quantum secret sharing schemes.

Contribution

It introduces methods to identify bipartite entanglement in graph states and shows that AME graph states can be used for quantum secret sharing with various access structures.

Findings

AME graph states exist for all number of parties

Methods to determine bipartite entanglement in graph states

Application of AME graph states in quantum secret sharing

Abstract

Absolutely maximally entangled (AME) states are multipartite entangled states that are maximally entangled for any possible bipartition. In this paper, we study the description of AME states within the graph state formalism. The graphical representation provides an intuitive framework to visualize the entanglement in graph states, which makes them a natural candidate to describe AME states. We show two different methods of determining bipartite entanglement in graph states and use them to define various AME graph states. We further show that AME graph states exist for all number of parties, and that any AME graph states shared between an even number of parties can be used to describe quantum secret sharing schemes with a threshold or ramp access structure directly within the graph states formalism.