Geometry of symmetric and noninvertible Pauli channels

Abstract

We analyze the geometry of positive and completely positive, trace-preserving Pauli maps that are fully determined by up to two distinct parameters. This includes five classes of symmetric and noninvertible Pauli channels. Using the Hilbert-Schmidt metric in the space of the Choi-Jamio\l{}kowski states, we compute the relative volumes of entanglement breaking, time-local generated, and divisible channels. Finally, we find the shapes of the complete positivity regions in relation to the tetrahedron of all Pauli channels.