Multipartite mixed maximally entangled states: mixed states with entanglement 1

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 and deriving a set of necessary and sufficient conditions for their existence. Additionally, we give worked examples and provide a large collection of tabulated multipartite MME states in a variety of systems. 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.