Multipartite Mixed Maximally Entangled States: Mixed States with Entanglement 1

TL;DR

This paper defines multipartite mixed maximally entangled (MME) states, extending bipartite concepts using multipartite Schmidt decomposition, and highlights their potential applications and significance in quantum information processing.

Contribution

It introduces a comprehensive definition of multipartite MME states, generalizing existing bipartite definitions and characterizing states with maximal entanglement across all decompositions.

Findings

MME states have entanglement 1 in all decompositions

Multipartite MME states extend bipartite concepts using Schmidt decomposition

Potential applications in remote state preparation

Abstract

We present a full definition of mixed maximally entangled (MME) states for multipartite systems, generalizing their existing definition for bipartite systems by using multipartite Schmidt decomposition. MME states are a special kind of maximally entangled mixed state (MEMS) for which every pure decomposition state in all decompositions is maximally entangled. Thus, MME states have entanglement 1 by all valid unit-normalized entanglement measures, whereas general MEMS can have entanglement less than 1. Multipartite MME states likely have important applications such as remote state preparation, and also set critical performance goals for entanglement measures.