Almost-idempotent quantum channels and approximate $C^{\ast }$-algebras

Alexei Kitaev

Let $\Phi$ be a unital completely positive (UCP) map on the space of operators on some Hilbert space. We assume that $\Phi$ is $\eta$-idempotent, namely, $\Vert {\Phi }^2-\Phi {\Vert }_{\mathrm{cb}}\le \eta$, and…