Classical structures of CP maps are all canonical

Stefano Gogioso

Classical structures of CP maps are all canonical

Quantum Physics 2021-11-01 v2

Authors: Stefano Gogioso

Abstract

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

Cite

@article{arxiv.1809.03466,
  title  = {Classical structures of CP maps are all canonical},
  author = {Stefano Gogioso},
  journal= {arXiv preprint arXiv:1809.03466},
  year   = {2021}
}

Comments

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 This article is superseded by arXiv:2110.07074

Classical structures of CP maps are all canonical

Abstract

Cite

Comments

Related papers