U(1)-symmetric dynamics without environmental coherence yields phase-covariant maps, and a three-qubit XY protocol is proposed to achieve Gibbs-preserving maps, but the construction's fixed-point algebra appears inconsistent.
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Hierarchy of Qubit Dynamical Maps in the Presence of Symmetry and Coherence
U(1)-symmetric dynamics without environmental coherence yields phase-covariant maps, and a three-qubit XY protocol is proposed to achieve Gibbs-preserving maps, but the construction's fixed-point algebra appears inconsistent.