Absolute Maximal Entanglement and Quantum Secret Sharing

TL;DR

This paper investigates absolutely maximally entangled states in quantum mechanics, introduces a new parallel teleportation protocol, and establishes a link between AME states and quantum secret sharing schemes, broadening their applicability.

Contribution

It presents a novel parallel teleportation protocol utilizing AME states and proves the equivalence between AME states and quantum secret sharing schemes for any number of parties.

Findings

Introduces a parallel teleportation protocol with flexible partitioning.

Proves the equivalence between AME states and quantum secret sharing schemes.

Establishes the existence of AME states for arbitrary numbers of parties.

Abstract

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.