Geometry of Pauli maps and Pauli channels
Katarzyna Siudzińska · Physical Review A · 2019
We analyze the geometrical properties of trace-preserving Pauli maps. Using the Choi-Jamio\l{}kowski isomorphism, we express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the Pauli map. We analytically compute the volumes of positive, trace-preserving Pauli maps and Pauli channels. In particular, we find the relative volumes of the entanglement-breaking Pauli channels as well as the channels that can be generated by a time-local generator. Finally, we show what part of the Pauli channels are $\mathrm{P}$- and $\mathrm{CP}$-divisible, which is related to the notion of Markovianity.