Local unitary equivalence of absolutely maximally entangled states constructed from orthogonal arrays

TL;DR

This paper investigates the classification of absolutely maximally entangled states using invariants, revealing infinitely many inequivalent states for certain multipartite configurations based on orthogonal arrays.

Contribution

It establishes a link between orthogonal arrays and the existence of infinitely many local unitary inequivalent AME states, advancing understanding of multipartite entanglement classification.

Findings

Infinitely many inequivalent three-party AME states for d > 2

Infinitely many five-party AME states for d ≥ 2

Existence of special orthogonal arrays implies multiple entanglement classes

Abstract

The classification of multipartite entanglement is essential as it serves as a resource for various quantum information processing tasks. This study concerns a particular class of highly entangled multipartite states, the so-called absolutely maximally entangled (AME) states. These are characterized by maximal entanglement across all possible bipartitions. In particular we analyze the local unitary equivalence among AME states using invariants. One of our main findings is that the existence of special irredundant orthogonal arrays implies the existence of an infinite number of equivalence classes of AME states constructed from these. In particular, we show that there are infinitely many local unitary inequivalent three-party AME states for local dimension $d > 2$ and five-party AME states for $d \geq 2$.