Axiomatic description of mixed states from selinger's CPM-construction

We recast Selinger's CPM-construction of mixed states completely positive maps [P. Selinger (2007) Dagger compact closed categories and completely positive maps. In: Proceedings of the 3rd International Workshop on Quantum Programming Languages (QPL 2005), Electronic Notes in Theoretical Computer Science 170, 139–163. Available from Peter Selinger&amp;apos;s homepage] as an axiomatization of maximally mixed states. This axiomatization also guarantees categories of completely positive maps to satisfy the preparation-state agreement axiom of [Coecke, B. (2007) De-linearizing linearity: projective quantum axiomatics from strong compact closure. In: Proceedings of the 3rd International Workshop on Quantum Programming Languages (QPL 2005), Electronic Notes in Theoretical Computer Science 170, 49–72. E-print: arXiv:quant-ph/0506134</p