纠缠及纠缠之外的量子关联刻画

项目名称： 纠缠及纠缠之外的量子关联刻画

项目编号： No.11301312

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 郭钰

作者单位： 山西大同大学

项目金额： 22万元

中文摘要： 量子纠缠在迅猛发展的量子信息科学领域中起着非常关键的作用，成为该领域中的一个非常活跃的研究课题。然而，除双量子比特(two-qubit)和双量子三比特(two-qutrit)系统外至今还没有既便于实际应用又为充要条件的纠缠判据。本项目拟以算子代数、算子理论为主要工具，试图从Hilbert 张量积空间上的算子交换性角度入手解决如下问题：(1) 给出既相对便于应用又是充要条件的纠缠判据并由所得判据导出新的纠缠度；(2)在此基础上刻画纠缠之外的量子关联以及各种量子关联的演化规律，从而比较系统地对量子态的非经典性质给出刻画；(3) 进而探讨更一般的Hilbert 张量积空间上的 Schatten-p 类正算子的类似于量子态纠缠的性质。

中文关键词： 纠缠；量子关联；Hilbert 空间；不可扩张纠缠基；量子相干

英文摘要： Entanglement is a very active research subject in the era of rapid development of quantum information science since it plays an important and key role in this field. However, except for the two-qubit and two-qutrit systems,there is no any criterion which not only can detect all entangled states but also is easy to handle. In this project, by exerting methods from operator algebra and operator theory, we attempt to investigate entanglement problem from the perspective of commutativity of the operators acting on the tensor product of Hilbert space. In this project we attempt to address the following problems:(1) propose a both easy-operational and necessary-sufficient entanglement criterion and then deduce a new entanglement measure from the obtained criterion; On the basis of the obtained results, (2) characterize quantum correlations beyond entanglement and the dynamics of these quantum correlations; and then (3) discuss the "entanglement property" of positive Schatten-p class operators acting on tensor product of Hilbert spaces.

英文关键词： Entanglement；Quantum correlation；Hilbert space；Unextendible entangled basis；quantum coherence