量子映射与量子态的对偶性
On duality between quantum maps and quantum states
摘要：
我们研究了量子操作的空间，以及更大的映射空间，这些映射是正的，但不是完全正的。提出了可分解性的一个构造性判据。定义并分析了一类由扩维酉矩阵确定的单随机运算。利用动力学矩阵和Jamiolkowski同构的概念，我们探讨了量子操作（动力学）和密度矩阵作用于扩展希尔伯特空间（运动学）之间的关系。在经典映射和离散概率分布的扩展空间之间建立了一种类似的关系。
英文摘要：
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is defined and analyzed. Using the concept of the dynamical matrix and the Jamiolkowski isomorphism we explore the relation between the set of quantum operations (dynamics) and the set of density matrices acting on an extended Hilbert space (kinematics). An analogous relation is established between the classical maps and an extended space of the discrete probability distributions.
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