  We study extensions of the mappings arising in usual Channel-State duality to
the case of Hilbert spaces with a direct sum structure. This setting arises in
representations of algebras with centers, which are commonly associated with
constraints, and it has many physical applications from quantum many-body
theory to holography and quantum gravity. We establish that there is a general
relationship between non-separability of the state and the isometric properties
of the induced channel. We also provide a generalisation of our approach to
algebras of trace-class operators on infinite dimensional Hilbert spaces.
