Pauli semigroups and unistochastic quantum channels

TitlePauli semigroups and unistochastic quantum channels
Publication TypeJournal Article
Year of Publication2019
AuthorsPuchała Z, Rudnicki Ł, Życzkowski K
JournalPhysics Letters A
Volume383
Issue20
Pagination2376-2381
Abstract

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.

URLhttps://arxiv.org/abs/1903.12448

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