Multipartite Entanglement Measure : Genuine to Absolutely Maximally Entangled

TL;DR

This paper introduces a new measure for multipartite entanglement that distinguishes between Genuinely Multipartite Entanglement and Absolutely Maximally Entangled states, aiding classification of four-partite systems.

Contribution

A novel entanglement measure is proposed that quantifies GME and AME states, with demonstrated robustness in classifying four-partite entangled states.

Findings

The measure effectively differentiates GME and AME states.

Application to four-partite systems shows accurate classification.

The measure is robust across various examples.

Abstract

Multipartite entanglement is a fundamental aspect of quantum mechanics, crucial to advancements in quantum information processing and quantum computation. Within this field, Genuinely Multipartite Entanglement (GME), being entangled in all bipartitions, and Absolutely Maximally Entanglement (AME), maximally entangled in all bipartitions, represent two significant types of entanglement with diverse applications. In this work, we introduce a new measure called the GME-AME multipartite entanglement measure, with a non-zero value representing the GME states and the maximum value is reached only by the AME states. The measure is applied to study the multipartite entanglement of four partite systems using the operator to state mapping, and the four partite permutation qutrit states are classified according to the measure. With various examples, we show that our measure is robust in classifying the four partite entangled states.