The Foundation of Mathematical Statistics on Quantum Inference and Its Applications

量子推理的数理统计基础及其应用

基本信息

批准号：
14204006
负责人：
AKAHIRA Masafumi
金额：
$ 29.7万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

项目摘要

The statistical investigation on various themes was done as follows. (1) Involving a relationship between statistical models and statistics, the properties of the models were discussed and some interesting results on the behavior of various statistics are obtained. (2) In the theory of statistics to finance, time series and their applications, statistical procedures were shown to be asymptotically useful. (3) In the experimental design and its related area, the mathematical structure is clarified by combinatorial procedures, and results intended to apply to practical problems were obtained. (4) In statistical sequential inference, some sequential procedures were proposed, and their properties were discussed in details. The asymptotic efficiencies were shown. (5) The construction of mathematically fundamental theory of biostatistics is tried, and statistically inferential procedures are shown to play an important role. In particular, bioassay test, score test etc. were shown to be usefu … More l. (6) The relationship between non-locality in quantum mechanics and statistical inference is clarified, and inferential procedures is also shown to be efficient in quantum estimation and quantum test. Further, it is recognized to play an important role as the theoretical base of concrete physical phenomena. (7) In statistical inference, on the lower bound for tail probabilites of consistent estimators, the first and second order asymptotic efficiencies are investigated from a different viewpoint from conventional Bahadur efficiency. And in order to unify both of non-parametric and parametric tests, the mathematical setup was done, new test statistics based on estimators of spectral density matrics were proposed, and their asymptotic properties are derived. (8) Under a family of non-parametric quantum states, state estimation, prediction of quantum state, quantum information geometry and discrimination problem on quantum states are trated, and new interesting results were obtained. Many symposium on the above were held and active discussion and mutual exchange of information were also done. Their results were summarized as a volume. Less

对各种主题的统计投资如下完成。（1）涉及统计模型与统计之间的关系，讨论了模型的特性，并获得了各种统计行为的一些有趣的结果。（2）在财务，时间序列及其应用的统计理论中，统计程序被证明在不对称上有用。（3）在实验设计及其相关区域中，通过组合程序阐明了数学结构，并获得了旨在应用于实际问题的结果。（4）在统计顺序推断中，提出了一些顺序程序，并详细讨论了它们的特性。显示了不对称效率。（5）尝试了数学上基本的生物统计学理论的构建，并显示出统计学上推论的程序起着重要作用。特别是，生物测定测试，得分测试等很有用……更多。（6）阐明了量子力学中的非局部性与统计推断之间的关系，推论程序在量子估计和量子测试中也有效。此外，它被认为是具体物理现象的理论基础的重要作用。（7）在统计推断中，在一致的估计量的尾部问题主义者的下限上，从常规巴哈杜尔效率的不同观点研究了第一阶和二阶渐近效率。为了统一非参数和参数测试，提出了基于光谱密度矩阵的估计值的新测试统计数据，并得出了其不对称性能。（8）在一个非参数量子状态的家族中，对量子状态的量子状态，量子状态的预测，量子信息几何形状和歧视问题进行了修改，并获得了新的有趣结果。举行了许多关于上述研讨会的研讨会，并进行了积极的讨论和信息的相互交流。他们的结果总结为卷。较少的