  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.
