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

Operator Structures and Quantum One-Way LOCC Conditions