arXiv 1302.46542013-02-19quant-phmath-phmath.MP

有限维Hilbert空间中的量子纠缠

Quantum entanglement in finite-dimensional Hilbert spaces

Szilárd Szalay

备注：: Ph.D. dissertation, 162 pages. It covers, it slightly improves, and it presents the material of the papers http://arxiv.org/abs/0807.1804, http://arxiv.org/abs/1101.3256, http://arxiv.org/abs/1105.3086 and http://arxiv.org/abs/1206.6253 in a unified treatment. Apart from those, a review of 40 pages on qualification and quantification of entanglement is given as introduction

摘要：

在过去的几十年里，量子纠缠被认为是量子信息理论的基础。一个基本的需要是理解它的定性和定量：量子态是纠缠的吗？如果是，那么它携带了多少纠缠？这些问题引入了可分性准则和纠缠度量，这两个问题都是基于多体纠缠的分类问题。在这篇论文中，在回顾了有限维希尔伯特空间的这三个基本主题之后，我提出了我对知识的贡献。我的主要结果是阐述的部分分离性分类的量子系统的混合状态组成的任意数量的子系统的任意维的希尔伯特空间。这个问题对于纯态来说很简单，但是对于混合态，它还没有被完全详细地考虑过。我不仅给出了分类，而且给出了这些类的充分必要的准则，这些准则使得确定一个混合状态属于哪一类成为可能。此外，这些标准是由测量纠缠的量的消失给出的。除此之外，我还介绍了一些与混合态纠缠有关的副结果。这些结果都是在学习阶段得到的，并给出了一些说明和例子。

英文摘要：

In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and if it is, then how much entanglement is carried by that? These questions introduce the topics of separability criteria and entanglement measures, both of which are based on the issue of classification of multipartite entanglement. In this dissertation, after reviewing these three fundamental topics for finite dimensional Hilbert spaces, I present my contribution to knowledge. My main result is the elaboration of the partial separability classification of mixed states of quantum systems composed of arbitrary number of subsystems of Hilbert spaces of arbitrary dimensions. This problem is simple for pure states, however, for mixed states it has not been considered in full detail yet. I give not only the classification but also necessary and sufficient criteria for the classes, which make it possible to determine to which class a mixed state belongs. Moreover, these criteria are given by the vanishing of quantities measuring entanglement. Apart from these, I present some side results related to the entanglement of mixed states. These results are obtained in the learning phase of my studies and give some illustrations and examples.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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