Complete Positivity for Mixed Unitary Categories

In this article we generalize the $\CP^\infty$-construction of dagger monoidal categories to mixed unitary categories. Mixed unitary categories provide a setting, which generalizes (compact) dagger monoidal categories and in which one may study quantum processes of arbitrary (infinite) dimensions. We show that the existing results for the $\CP^\infty$-construction hold in this more general setting. In particular, we generalize the notion of environment structures to mixed unitary categories and show that the $\CP^\infty$-construction on mixed unitary categories is characterized by this generalized environment structure.

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