【作者】 张林；

【导师】 武俊德；

【作者基本信息】 浙江大学 ， 基础数学， 2012， 博士

【摘要】 引起量子系统的一个变化,我们称为是一个量子操作.这种变化既可能有益,但却常常不利,因为它将引起量子系统退相干.量子信息区别于经典信息的本质特征恰恰在于系统的相干性.因而将量子操作对系统的影响予以量化是量子信息理论研究的一个核心问题.本文重点研究了量子操作熵的动态可加性、保持von Neumann熵之量子操作的刻画、两体量子态中的关联以及Holevo量的上界等问题.主要内容为：一、量子操作熵的动态可加性研究.借助于量子态的保熵延拓技巧,刻画了两个量子操作的复合操作熵的可加性特征.对量子操作引入双正交概念,以此为基础研究了三个量子操作的复合操作熵的强可加性.二、保持、on Neumann熵之量子操作的刻画问题.以量子相对熵的表示为工具,结合Petz关于相对熵的单调性不等式成为等式的条件,加之量子操作的不动点性质,刻画了保持von Neumann熵之量子操作的特征.三、两体量子态的关联问题.借助于量子操作的Stinespring表示得到了经典关联的上界,回答了这方面的一个猜测.以量子熵的Lindblad不等式为工具并结合三体量子态的强可加性,得到了量子关联的上界.四、Holevo量的上界问题.给出了两体系统的量子态在实施一类量子操作后所得到的量子系综的Holevo量的上界.以酉算子构成的分块矩阵的半正定性特征为工具,研究了W. Roga等人提出的关于三个量子态所构成之系综的Holevo量的上界问题.更多还原

【Abstract】 The changes, for instance, decoherence, occurred over a quantum system, which is generally induced by quantum operations on the quantum system. It distinguishes between classical information theory and quantum information theory. Hence quan-tifying the changes induced over a quantum system by quantum operations is an important problem in quantum information theory.In this thesis, we study several important problems such as the dynamical addi-tivity and strong dynamical additivity of quantum operations, the characterizations of von Neumann entropy-preserving quantum operations, classical and quantum cor-relations in bipartite states and the upper bound of the Holevo quantity. The main content is the following:Firstly, we study the dynamical additivity and strong dynamical additivity of quantum operations. Extension of quantum states without changing its entropy to a larger quantum system is employed to characterize the additivity of map entropy for the composite quantum operations. Then we introduce notion of bi-orthogonality within quantum operations and based on it, we investigate the strong dynamical additivity of quantum operations.The second part devotes to characterizations of von Neumann entropy-preserving quantum operations. We represent the von Neumann entropy of a quantum state as the relative entropy between the target state and the full mixed state. By the satu-ration of Petz’s monotonicity condition of relative entropy and the property of fixed points of quantum operations, we give a complete characterization of von Neumann entropy-preserving unital quantum operations. As a consequence, Poritz’s classical version of corresponding Shannon entropy preserving bi-stochastic matrices can be easily derived from our results.Thirdly, we give an upper bound on the classical correlations in bipartite states in terms of quantum operation language. We also study the quantum correlations in bipartite states by making essential use of the Lindblad inequality and the structure of strong additivity states.Finally, we investigate the upper bound of the Holevo quantity. In the last part of the thesis, we generalize an important inequality which is appeared in the previous chapter. Then we utilize it to construct a bipartite state to prove a conjecture, proposed by W. Roga, on upper bound of the Holevo quantity.更多还原