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Statistical Theory of Quantum Information Processing

量子信息处理统计理论

基本信息

批准号：
EP/E052290/1
负责人：
Madalin Guta
金额：
$ 48.53万
依托单位：
University of Nottingham
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FE052290%2F1
关键词：
Statistical Theory Quantum Information Processing

项目摘要

The inference of an unknown parameter from random data whose probability distribution depends on that parameter, is a central topic in Statistics. Here are a few motivating questions of this proposal.How do we quantify the amount of statistical information stored in an atom or a photon whose state depends on an unknown parameter ? How does this information change when we manipulate the system ? How much information can we extract if we measure the system and obtain random data consisting of measurement results ? The guiding principle of the proposal is that quantum systems carry an intrinsic statistical information and the aim is to develop new statistical methods dealing with the processing of this type of quantum information. The goal is to extend the framework of Quantum Statistics established by Helstrom and Holevo in the seventies, by opening new directions motivated by the technological advances in Quantum Engineering and modern developments in Mathematical Statistics. The project is organised in three main topics. The first topic aims at developing a Quantum Statistical Decision Theory which roughly speaking, is the general mathematical framework for answering the motivating questions. The novelty of this theory is that it looks at the intrinsic structure of quantum statistical models and all transformations between them, rather than always reducing them to classical statistical models through measurements. The second topic aims at constructing more accurate estimation tools for quantum systems whose states are determined by an infinite number of parameters, such as the light in a cavity. The techniques are inspired by state-of-the-art methods in non-parametric statistics and will benefit experimentalists by providing them with accurate and reliable estimators based on a limited number of measurements. This is very relevant for Quantum Engineering where the creation of a new and exotic quantum state is confirmed using statistical estimation methods. The third topic aims at developing statistical methods for the set-up of continuous-time measurements. This is the proper physical framework for dealing with dissipation, which is a main concern in Quantum Computation. Recent state-of-the-art experiments have shown that Quantum Feedback Control is a valuable tool in Quantum Metrology and Quantum Engineering. However it is only partially understood how statistical uncertainties influence the stability of the dynamical models, and a mathematical analysis of parameter estimation problems has still to be developed.In conclusion, the project opens a new area of research across Mathematical Statistics, Quantum Information and Quantum Filtering & Control, with deep and interesting mathematical problems and very close connection to the latest developments in Experimental Physics, making it a very timely research programme.

从随机数据中推断未知参数，其概率分布取决于该参数，这是统计学中的一个中心主题。以下是该提案的几个激励问题。我们如何量化存储在一个原子或光子中的统计信息量，它们的状态取决于一个未知的参数？当我们操纵系统时，这些信息是如何变化的？如果我们测量系统并获得由测量结果组成的随机数据，我们可以提取多少信息？该建议的指导原则是量子系统携带一种内在的统计信息，其目的是开发新的统计方法来处理这种类型的量子信息。目标是扩展Helstrom和Holevo在70年代建立的量子统计框架，在量子工程技术进步和数理统计的现代发展的推动下开辟新的方向。该项目分为三个主要主题。第一个主题旨在发展量子统计决策理论，粗略地说，这是回答激励问题的一般数学框架。这一理论的新颖之处在于，它着眼于量子统计模型的内在结构以及它们之间的所有转换，而不是总是通过测量将它们还原为经典统计模型。第二个主题旨在为量子系统构建更精确的估计工具，这些系统的状态由无限数量的参数决定，例如腔中的光。这些技术受到非参数统计中最先进方法的启发，并将为实验人员提供基于有限数量测量的准确可靠的估计器，从而使他们受益。这与量子工程非常相关，在量子工程中，使用统计估计方法确认了新的奇异量子态的创建。第三个主题旨在发展连续时间测量设置的统计方法。这是处理耗散的适当物理框架，耗散是量子计算中的一个主要问题。最近的实验表明，量子反馈控制在量子计量和量子工程中是一种有价值的工具。然而，统计不确定性如何影响动力学模型的稳定性只是部分了解，参数估计问题的数学分析仍有待发展。总之，该项目开辟了一个跨越数理统计、量子信息和量子滤波与控制的新研究领域，具有深刻而有趣的数学问题，并与实验物理学的最新发展密切相关，使其成为一个非常及时的研究项目。