Completely positive projections and biproducts

Understand

The recently introduced CP*-construction unites quantum channels and classical systems, subsuming the earlier CPM-construction in categorical quantum mechanics.

• We compare this construction to two earlier attempts at solving this problem: freely adding biproducts to CPM, and freely splitting idempotents in CPM.
• The CP*-construction embeds the former, and embeds into the latter, but neither embedding is an equivalence in general.