01400nas a2200157 4500000000100000000000100001008004100002100002200043700002100065700002200086245005600108856003700164300001400201490000800215520101900223 2019 d1 aZbigniew Puchała1 aŁukasz Rudnicki1 aKarol Życzkowski00aPauli semigroups and unistochastic quantum channels uhttps://arxiv.org/abs/1903.12448 a2376-23810 v3833 a

We adopt the perspective of similarity equivalence, in gate set tomography called the gauge, to analyze various properties of quantum operations belonging to a semigroup, Φ=e^{Lt},and therefore given through the Lindblad operator. We first observe that the non unital part of the channel decouples from the time evolution. Focusing on unital operations we restrict our attention to the single-qubit case, showing that the semigroup embedded inside the tetrahedron of Pauli channels is bounded by the surface composed of product probability vectors and includes the identity map together with the maximally depolarizing channel. Consequently, every member of the Pauli semigroup is unitarily equivalent to a unistochastic map, describing a coupling with one-qubit environment initially in the maximally mixed state, determined by a unitary matrix of order four.