Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices

TL;DR

This paper explores the construction of Absolutely Maximally Entangled (AME) states, their connection to combinatorial designs, and introduces the concept of multi-unitarity, enhancing understanding of multipartite entanglement in quantum information.

Contribution

It provides new constructions of AME states, links them to combinatorial designs, and introduces the concept of multi-unitarity for tensors in quantum states.

Findings

New constructions of AME states linked to combinatorial designs

Identification of multi-unitarity as a key property of AME states

Potential applications in quantum teleportation and holography

Abstract

Absolutely Maximally Entangled (AME) states are those multipartite quantum states that carry absolute maximum entanglement in all possible partitions. AME states are known to play a relevant role in multipartite teleportation, in quantum secret sharing and they provide the basis novel tensor networks related to holography. We present alternative constructions of AME states and show their link with combinatorial designs. We also analyze a key property of AME, namely their relation to tensors that can be understood as unitary transformations in every of its bi-partitions. We call this property multi-unitarity.