We generalize an example of Jochym-O'Connor et. al., showing that it is possible for a quantum to channel to privatize information, even it if it admits no private subspaces.

We show how privacy is connected to the concept of quasiorthogonality of algebras, and with the aid of ideas from group theory, show how Pauli channels can privatize information in the absence of private subspaces.

Coauthors: Tomas Jochym-O'Connor, David Kribs, Raymond Laflamme, Rajesh Pereira