We study a family of quantum Markov semigroups with circulant structure. We obtain a complete description of the spectral representation for the Lindbladian and, putting it together with some purely probabilistic properties of a classical associated process, we can study asymptotic properties, invariant states, quantum-detailed balance conditions and reducibility. In particular, in the reducible case, we can construct a generator on a lower-dimensional space which can fully describe the original circulant semigroup.

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循环量子过程的结构和块表示

我们研究了一族具有循环结构的量子马尔可夫半群。我们获得了 Lindbladian 光谱表示的完整描述，并将其与经典相关过程的一些纯概率性质放在一起，我们可以研究渐近性质、不变状态、量子详细平衡条件和可还原性。特别是在可约情况下，我们可以在一个低维空间上构造一个能完全描述原始循环半群的生成器。