量子关联与量子态的区分

发布时间：2018-04-30 14:41

本文选题：量子测量 + 量子纠缠　；参考：《浙江大学》2016年博士论文

【摘要】：系统之间的关联是自然界中的一个普遍现象.量子关联是量子信息处理与量子计算技术必不可少的重要资源,有其自身规律性和深刻性.量子纠缠是量子系统间最重要和最神秘的一类关联.本文重点研究了量子态纠缠度量的分解性质、量子失协的分解性质、任意量子测量与之相伴随的可恢复测量的构造、量子态的区分等问题.主要内容为：一、量子态之间的局部正交性和纠缠度量的分解.首先将量子纯态之间的局部正交概念推广到一般的混合量子态,研究了量子态在局部正交混合量子态分解意义下,纠缠形成、纠缠成本、纠缠提纯的分解性质,将Horodecki关于纯态分解的结论推广到一般的混合态分解情况.最后给出例子说明本章主要结果的条件确实存在.二、量子失协的可分解性.得到了量子失协可分解的易于判断的充分条件,进一步地,我们说明了在此条件下,量子失协完全由量子纠缠形成所得到.三、一类可恢复测量的构造.对于任意给定的冯·诺伊曼测量,我们构造了与之相伴随的可恢复测量；进一步地,我们建立了这两个测量所诱导的冯.诺伊曼熵与量子失协之间的密切关系.四、量子态的有歧区分和无歧区分的混合形式.对于给定的三个量子态,我们建立了这三个量子态的有歧区分和无歧区分的混合形式,证明了这个新的区分方法较之于已知的区分方法有更高的成功概率.
[Abstract]:The connection between systems is a common phenomenon in nature. Quantum correlation is an essential resource in quantum information processing and quantum computing. It has its own regularity and profundity. Quantum entanglement is one of the most important and mysterious relationships among quantum systems. In this paper, we focus on the decomposition properties of quantum state entanglement metrics, the decomposition properties of quantum disconnection, the construction of recoverable measurements associated with arbitrary quantum measurements, the differentiation of quantum states, and so on. The main contents are as follows: first, the local orthogonality between quantum states and the decomposition of entanglement metric. Firstly, the concept of local orthogonality between pure quantum states is extended to the general mixed quantum states. The entanglement formation, entanglement cost, and the decomposition properties of entanglement purification are studied in the sense of local orthogonal mixed quantum state decomposition. Horodecki's conclusion on pure state decomposition is extended to general mixed state decomposition. Finally, an example is given to show that the main results of this chapter do exist. Second, the decomposability of quantum disconnection. A sufficient condition is obtained for the decomposition of quantum disconnection, which is easy to judge. Furthermore, we show that quantum disconnection is completely formed by quantum entanglement under this condition. Third, a class of recoverable structures. For any given von Neumann measurements, we construct recoverable measurements associated with them, and further, we establish the von induced by these two measurements. The close relationship between Neumann entropy and quantum disconnection. Fourth, the mixed forms of quantum states with and without disambiguation. For a given three quantum states, we establish the mixed forms of disambiguation and disambiguation of these three quantum states, and prove that this new discrimination method has a higher probability of success than the known discrimination method.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413.1

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