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Absolute Maximal Entanglement and Quantum Secret Sharing
Wolfram Helwig, Wei Cui, Arnau Riera, José I. Latorre, Hoi-Kwong Lo
TL;DR
The paper asks how absolutely maximally entangled states can support multipartite quantum-information tasks and whether they exist for arbitrary party counts. It introduces parallel teleportation protocols and establishes a correspondence with pure-state quantum secret sharing, yielding existence results for suitable qudit dimensions.
Problem
Understanding of multipartite entanglement becomes poorer as the number of local quantum degrees of freedom increases, while the applications and existence of AME states remain limited for qubits.
Method
The paper defines AME states, develops parallel teleportation protocols, and relates even-party AME states one-to-one with pure-state threshold quantum secret-sharing schemes.
Results
AME states support teleportation with sender and receiver partitions chosen after distribution, and the QSS correspondence proves AME-state existence for arbitrary party counts with appropriate qudit dimensions.
Takeaways & Limitations
AME states provide multipartite communication resources with flexible sender–receiver assignments and connect entanglement constructions to quantum secret sharing.
Abstract
from arXiv · showhide
We study the existence of absolutely maximally entangled (AME) states in quantum mechanics and its applications to quantum information. AME states are characterized by being maximally entangled for all bipartitions of the system and exhibit genuine multipartite entanglement. With such states, we present a novel parallel teleportation protocol which teleports multiple quantum states between groups of senders and receivers. The notable features of this protocol are that (i) the partition into senders and receivers can be chosen after the state has been distributed, and (ii) one group has to perform joint quantum operations while the parties of the other group only have to act locally on their system. We also prove the equivalence between pure state quantum secret sharing schemes and AME states with an even number of parties. This equivalence implies the existence of AME states for an arbitrary number of parties based on known results about the existence of quantum secret sharing schemes.