标题： 量子马尔可夫链的渐近性质 显示英文标题

标题： Asymptotic properties of quantum Markov chains

摘要： 研究了由最一般的物理相关量子操作生成的量子马尔可夫链的渐近动力学。 结果表明，它被限制在一个吸引子空间上，在该空间上得到的量子马尔可夫链是可以对角化的。 提出了一种构造该吸引子空间基底及其相关对偶基底的程序。 当存在一个严格正的量子态时，无论该量子操作是收缩该态还是使其保持不变，该构造均适用。 此外，还推导出了吸引子空间与量子马尔可夫链定义中涉及的克劳斯算符之间的代数关系。 这种构造不仅有望在希尔伯特空间维数较大而吸引子空间维数较小时提供重要的计算优势，而且也为量子马尔可夫链的渐近动力学与其生成量子操作的不动点之间的关系提供了新的见解。 显示英文摘要

摘要： The asymptotic dynamics of quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space on which the resulting quantum Markov chain is diagonalizable. A construction procedure of a basis of this attractor space and its associated dual basis is presented. It applies whenever a strictly positive quantum state exists which is contracted or left invariant by the generating quantum operation. Moreover, algebraic relations between the attractor space and Kraus operators involved in the definition of a quantum Markov chain are derived. This construction is not only expected to offer significant computational advantages in cases in which the dimension of the Hilbert space is large and the dimension of the attractor space is small but it also sheds new light onto the relation between the asymptotic dynamics of quantum Markov chains and fixed points of their generating quantum operations.