G-Circulant Quantum Markov Semigroups.

This article focuses on the extension and analysis of circulant Quantum Markov Semigroups (QMSs) to a broader class called left G-circulant QMSs, where G is an arbitrary finite group. It introduces left G-circulant Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generators acting on matrix algebras associated with G, showing these generators admit block-diagonal representations determined by the subgroup H generated by the support of the defining vector. The work characterizes the structure, steady states, and asymptotic behavior of left G-circulant QMSs, proving that their preduals are also left G-circulant and providing explicit formulas for their time evolution. Additionally, it identifies a family of steady states common to all such QMSs, constructed from positive circulant matrices, and determines the limit points and domains of attraction of the semigroups under mild conditions. The article also discusses implications for quantum detailed balance, spectral gaps, decoherence-free subalgebras, and covariance properties within this generalized framework.