Operator Structures and Methods in Quantum Error Correction, Quantum Privacy, and Entanglement Theory

在现代科学的许多领域，我们正处在“量子革命”的门口，也许最重要的是基于量子信息科学的新型技术的发展。*量子信息是一个总括的术语，它已经发展到包括量子计算、量子密码学、量子信息理论和量子信息处理等学科。加拿大已将自己定位为这些理论和实验工作的世界领先者，特别是加拿大数学界在其最近的长期计划中将量子信息确定为一个关键研究领域。拟议研究的主要目标是研究量子信息的核心基础问题，方法植根于数学。具体地说，David Kribs提出的研究计划直接触及了这门学科的数学基础的核心；通过基于核心算符理论的数学结构和技术的方法论方法，加强和扩大了他在量子纠错、量子隐私和量子纠缠理论等基本领域的研究。*作为拟议研究的一部分，克里布斯还将继续努力培训这些新兴和成熟学科以及基础数学领域的高素质人员，并在与量子信息高度跨学科领域交叉的不同科学界之间产生互动。

We are on the doorstep of a “quantum revolution” in many areas of modern science, perhaps most significantly in the development of new types of technologies based on quantum information science. ******Quantum information is the umbrella term that has evolved to encompass such disciplines as quantum computing, quantum cryptography, quantum information theory, and quantum information processing. Canada has positioned itself as a world leader in these theoretical and experimental efforts, and the Canadian mathematical community in particular has identified quantum information as a key research area in its recent long range plan.*** ***The primary goal of the proposed research is to investigate central foundational problems in quantum information, with an approach rooted in mathematics. Specifically, the proposed research program of David Kribs goes directly to the heart of the mathematical foundations of the subject; intensifying and broadening his investigations in the fundamental areas of quantum error correction, quantum privacy, and quantum entanglement theory, with a methodological approach based on core operator theoretic mathematical structures and techniques. ******As part of the proposed research, Kribs will also continue his efforts in the training of highly qualified personnel in these emerging and maturing disciplines and the underlying mathematics, and at generating interactions between the different scientific communities that intersect with the heavily interdisciplinary areas of quantum information.