  We conduct the first detailed analysis in quantum information of recently
derived operator relations from the study of quantum one-way local operations
and classical communications (LOCC). We show how operator structures such as
operator systems, operator algebras, and Hilbert C*-modules all naturally arise
in this setting, and we make use of these structures to derive new results and
new derivations of some established results in the study of LOCC. We also show
that perfect distinguishability under one-way LOCC and under arbitrary
operations is equivalent for several families of operators that appear jointly
in matrix and operator theory and quantum information theory.
