量子信息区分

Quantum information discrimination is an important issue in quantum information science. It is significant for the development of quantum correspondence, to research the problems of quantum information discrimination. Unfortunately, this problem have not been completely solved until now. In this project, quantum mixed state unambigous discrimination and quantum operation discrimination will be reaseared. The detail contents are as follows. (1) We get some properties of the measurement operators by researching on the restrictive conditions in unambiguous discrinination scheme, then combining some arithmetical techniques, a upper bound on the maximum successs probability of any m quantum mixed states unambiguous discrimination will be presented. Furthermore, we consider the relationship between the new upper bound and the other existing bounds,the accessibility, and the application of the new upper bound. (2) We introduce a mapping function and some properties from operator to vector, then combining the spectral decomposition of positive operator and the Kraus form of operation, and using some arithmetical techniques, we propose a upper bound on the maximum successs probability of any m quantum operations ambiguous discrimination and unambiguous discrimination, respectively. Moreover, we analyze how these new bounds are attainable. We hope that these results are helpful for further research on quantum communication.

量子信息区分是量子通信领域中的基本问题。研究量子信息区分对量子通信的发展有着重要的理论意义和应用价值，然而目前这个问题却并没有解决好。本项目拟对量子信息区分中的量子混合态的无歧区分和量子运算的有歧区分与无歧区分进行研究,具体内容为:(1)拟通过研究无歧区分方案中对测量算子设计的制约关系，得出无歧区分测量算子的一些重要特性，再结合数学运算技巧，给出任意m个量子混合态无歧区分最大成功概率的新上界，并考虑新上界与已有上界的关系、可达性和应用情况；(2)拟通过引入算子到状态之间的一一映射和特性，结合正算子的谱分解形式和运算的Kraus表示形式，利用数学推导技巧，分别给出任意m个量子运算无歧区分和有歧区分的最大成功概率的上界，并研究其可达性。希望本项目的结果能为进一步研究量子通信提供帮助。

量子信息区分是量子通信领域中的基本问题,研究量子信息区分对量子通信的发展有着重要的理论意义和应用价值。本项目拟对量子信息区分中的量子混合态区分和量子运算区分进行研究,具体取得的成果为:通过引入算子到状态之间的一一映射和特性，结合正算子的谱分解形式和运算的Kraus表示形式，利用数学推导技巧，给出了任意m个量子运算有歧区分的最大成功概率的三个上界，这三个界中只包含要区分的量子运算的Kraus算子和先验概率，跟输入的状态无关，可为进一步研究量子信息区分的最大成功概率提供帮助。