Operator structures and quantum one-way LOCC conditions

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 naturally arise in this setting. We make use of these structures to derive new results and bounds in the study of one-way LOCC, and we use the approach to uncover new derivations of some previously established results.