论文标题
量子通道半群的吸收和固定点
Absorption and Fixed Points for Semigroups of Quantum Channels
论文作者
论文摘要
在目前的工作中，我们审查并完善了有关量子通道半群的固定点的一些结果。非共同的潜在理论使我们能够表明，复发性半群的固定点集是w*-ergebra。除了这种结果的内在兴趣外，它还通过吸收量（对吸收概率的非公共概括性概括）对固定点的研究有所改善：在假设吸收复发空间的假设（因此允许非暂时性瞬态空间）的假设下，我们可以在固定点设置和概率集合中的描述 - w*w w w w w w w w w*w*w************* - 此外，我们能够展示一个反复的半群的示例，该示例不接受希尔伯特空间分解为正交最小的不变域（相反，与经典的马尔可夫链和量子通道的正面复发的阳性复发相反）。
In the present work we review and refine some results about fixed points of semigroups of quantum channels. Noncommutative potential theory enables us to show that the set of fixed points of a recurrent semigroup is a W*-algebra; aside from the intrinsic interest of this result, it brings an improvement in the study of fixed points by means of absorption operators (a noncommutative generalization of absorption probabilities): under the assumption of absorbing recurrent space (hence allowing non-trivial transient space) we can provide a description of the fixed points set and a probabilistic characterization of when it is a W*-algebra in terms of absorption operators. Moreover we are able to exhibit an example of a recurrent semigroup which does not admit a decomposition of the Hilbert space into orthogonal minimal invariant domains (contrarily to the case of classical Markov chains and positive recurrent semigroups of quantum channels).
