Classical structures of CP maps are all canonical

Abstract

We use purity, a principle borrowed from the foundations of quantum information, to show that all isometric comonoids in the category $\mathrm{CPM}\left(\mathrm{fHilb}\right)$ are necessarily pure. As a corollary, we answer an open question about special dagger Frobenius algebras (and classical structures in particular) in $\mathrm{CPM}\left(\mathrm{fHilb}\right)$: we show that they are all canonical, i.e. that they all arise by doubling of special dagger Frobenius algebras from the category $\mathrm{fHilb}$.

The proof of theorem 2 relies on an unsubstantiated statement, a flaw which couldn't be directly rectified. This article is superseded by arXiv:2110.07074

References in corpus (1)

• Entangled and sequential quantum protocols with dephasing