CIF: Small: Learning Quantum Information Measures

量子信息处理系统正在变得实用，人们预计这些系统将在十年内很快商业化，并将成为我们日常生活的一部分。然而，我们对可以从量子系统中收集到的信息量的理解仍然非常初级。例如，学习量子态的基本问题(称为层析成像)的复杂性在过去几年才得到解决，而它对分布估计的经典模拟现在是任何统计学入门课程的教科书材料。该奖项下的研究将致力于研究基本信息度量的估计问题，以及为量子系统引入新的信息度量。该项目将建立量子信息系统信息处理能力的基本限制，并设计能够匹配这些限制的新算法。该项目的成果将有助于开发高效的量子计算机和通信系统。该奖项将加深对量子系统作为统计机制的理解，并融合表象理论、信息论、统计学和计算机科学等不同学科的思想。提出并发展了最大似然估计统计原理的一种新的变种，作为量子性质估计的一般方法。该项目还将研究将Schur-Weyl对偶的表示理论结果扩展到更高的维度，以获得多量子系统性质的最优量子测量方案。这项工作包括提出比文献中认为的理论上最优的测量方案更现实的测量方案，这些方案在实践中过于复杂，无法用现有技术实施。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum information processing systems are becoming practical with the expectation that these systems will soon be commercialized within a decade, and will be a part of our everyday life. However, our understanding of the amount of information that can be gleaned from a quantum system is still very rudimentary. For example, the complexity of the basic question of learning a quantum state (called tomography) was only resolved in the past few years, whereas its classical analogue of distribution estimation is now textbook material in any introductory statistics course. Research under this award will be dedicated to the study of the problem of estimating fundamental information measures, as well as introduce new information measures for quantum systems. The project will establish the fundamental limits of the information processing capabilities of quantum information systems, as well as design novel algorithms that can match these limits. The project outcomes can enable the development of efficient quantum computer and communication systems.The award will develop a deeper understanding of a quantum system as a statistical mechanism, and integrate ideas from various disciplines such as representation theory, information theory, statistics, and computer science. A novel variation of the statistical principle of maximum likelihood estimation as a general methodology for quantum property estimation will be proposed and developed. The project will also study the extension of representation theory results of Schur-Weyl duality to higher dimensions to obtain optimal quantum measurement schemes for properties of multiple quantum systems. The work includes proposing measurement schemes that are more realistic than the theoretically-optimal ones considered in the literature that in practice are too complex to be implemented with existing technology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.