【作者】 王银珠；

【导师】 侯晋川；

【作者基本信息】 太原理工大学 ， 固体力学， 2014， 博士

【摘要】 量子信息与量子计算是最近几十年迅速发展起来的一门新兴交叉学科,由于它有巨大的应用价值和重大的科学意义,已引起越来越多的物理学家、计算机学家、数学家以及许多领域专家学者的高度关注.量子纠缠是量子信息理论的一种重要物理资源,如何判断和量化两体或多体复合量子系统态的纠缠性以及纠缠度是非常重要的课题.在有限维情形,关于量子态的纠缠判据和纠缠度已获得很多有价值的结果.但是无限维复合系统中量子态的纠缠性探测以及纠缠度问题则要困难得多,目前已知结果甚少.另外对于有限维或无限维多体复合系统量子态的部分可分性的研究也属刚刚起步,特别是关于多体量子态的k-可分性,以及相对于k体分划的纠缠度的已知结果更少.本博士学位论文主要研究两体以及多体复合系统量子态的纠缠判据和纠缠度问题.主要结果如下：1.给出无限维两体以及多体复合系统量子态的一个迹不等式判据,并与约化判据做了比较；获得两种形式的无限维多体复合系统量子态的约化判据；针对2(?)∞和N (?)∞的情形,得到两个纠缠判据,推广了有限维情形的相关结果；基于局域正交可观测量,给出有限维多体量子态全可分的一些必要条件.2.研究多体复合系统量子态的k可分性,获得多体纯态k-可分的若干等价条件,给出有限维多体复合系统量子态k-可分的一些必要条件.3.引进有限维多体复合系统量子态相对于k-体分划的κ-ME EoF纠缠度以及κ-ME Negativity纠缠度概念,并证明其满足通常要求的纠缠度的性质,如：在k可分态上取值为0,局部酉操作不变性以及局部操作与经典通信不增性等.另外,还分别给出所给纠缠度的一个下界.4.将有限维多体复合系统量子态的几何纠缠度推广到无限维系统；给出有限维多体量子态的κ-ME Concurrence的一个上界.5.对于多体量子态,引进λk范数||·||λ(k),在此基础上定义多体系统量子态相对于k体分划的一种纠缠度,并证明其满足通常要求的纠缠度的性质.更多还原

【Abstract】 Quantum information and quantum computation is a newly emerging and fast developing cross subject in recent decade years, since it has tremendous application value and great scientific significance, this subject has attracted more and more noticed by physicists、computer scientists、mathematicians and many experts and scholars of other fields. Quantum entanglement is an important physical resource of quantum in-formation theory, how to detect entanglement and quantize entanglement amount for states in bipartite and multipartite quantum systems is a very important subject. In finite-dimensional cases, there are many valuable results about detecting entanglement and quantizing entanglement amount. But it is very difficult to detect separability and quantize entanglement amount for states in infinite-dimensional composite quantum systems, there is only a few results about these fields. In addition, the partial separa-bility for finite-dimensional or infinite-dimensional multipartite quantum states is just beginning to be developed, in particular, there is only a few results about k-separability and entanglement measurement relative to k-partition for multipartite quantum states.This doctoral thesis mainly study entanglement criteria and entanglement mea-surements for states in bipartite or multipartite quantum systems. The main research contents are as follows:1. We give a trace inequality criterion for states in infinite-dimensional bipartite and multipartite quantum systems, and make a comparison with reduction criterion; We give two class reduction criteria for states in infinite-dimensional multipartite quantum systems; For the case of2(?)∞and N(?)∞, we obtain two entanglement criteria, which generalized the results of finite-dimensional systems; We obtain some necessary conditions for fully separable multipartite quantum states based on local orthogonal observables.2. We study the k-separability for multipartite quantum states, and obtain some equivalent conditions for k-separable pure states in finite-or infinite-dimensional multi-partite quantum systems. Furthermore, some necessary conditions are presented about k-separable multipartite quantum states in finite-dimensional quantum systems.3. We introduce two new entanglement measurements,k-ME EoF and k-ME Neg-ativity with respect to k-partition in finite-dimensional multipartite quantum systems, and prove these measurements satisfy some necessary properties, such as, its value is zero for k-separable states, and it is invariant under local unitary transformations, and its entanglement amount cannot increase under local operations and classical commu-nication. In addition, we obtain a lower bound about k-ME EoF and k-ME Negativity, respectively.4. We generalized the geometry entanglement measure to infinite dimensional multipartite quantum systems. And then, we study the k-ME Concurrence measure, give a upper bound about k-ME Concurrence measure in finite-dimensional multipartite quantum systems.5.For multipartite quantum states, we introduce||·||γ(k), and define an entanglement measure for multipartite quantum states with respect to k-partition, and prove that it satisfies some basic properties of entanglement measure.更多还原