Absolutely maximally entangled pure states of multipartite quantum systems

TL;DR

This paper surveys methods for generating absolutely maximally entangled states in multipartite quantum systems, analyzing their entanglement properties and classification.

Contribution

It provides an updated overview of techniques beyond standard graph and stabilizer states, including new analyses of entanglement and state classifications.

Findings

Analyzed entanglement of reduced states from AME projectors

Studied states from symmetric superpositions of GHZ states

Summarized local unitary equivalence classes of AME states

Abstract

Absolutely maximally entangled (AME) pure states of a system composed of $N$ parties are distinguished by the property that for any splitting at least one partial trace is maximally mixed. Due to maximal possible correlations between any two selected subsystems these states have numerous applications in various fields of quantum information processing including multi-user teleportation, quantum error correction and secret sharing. We present an updated survey of various techniques to generate such strongly entangled states, including those going beyond the standard construction of graph and stabilizer states. Our contribution includes, in particular, analysis of the degree of entanglement of reduced states obtained by partial trace of AME projectors, states obtained by a symmetric superposition of GHZ states, an orthogonal frequency square representation of the "golden" AME state and an updated summary of the number of local unitary equivalence classes.