Quantum Information Theory

量子信息论

• 批准号: 0074566
• 负责人: Mary Beth Ruskai
• 金额: $ 5万
• 依托单位: University of Massachusetts Lowell
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2002-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0074566&HistoricalAwards=false
• 关键词: Quantum; Information; Theory

ABSTRACT The primary focus of this project is the study of a variety of mathematical problems in quantum computation and information theory. Although building quantum computers remains a formidable experimental challenge, they have the potential to efficiently handle problems whose computational complexity puts them beyond the scope of classical digital computers. Some aspects of this proposal, such as error correction and the exploration of multi-bit gates, are directly related to quantum computation. However, the main emphasis is on problems in the related area of quantum communication, particularly channel capacity, optimal encoding and decoding schemes and classification of entanglement. The P.I.'s past work on the analysis of multi-particle systems in strong magnetic fields, the properties of quantum-mechanical entropy, and maps on operator algebras provides a strong starting point for developing new mathematical tools needed to deal with these challenging issues. The possibility of using quantum computers to efficiently factoring large numbers, is a potential threat to the security of existing cryptographic protocols. Fortunately, using quantum particles for communication, which is more feasible experimentally, offers new mechanisms for distributing cryptographic keys as well as encoding messages and transmitting information. These include both procedures based on the transmission of quantum particles for encoding and sending information; and innovative new protocols, based on a quantum phenomenon known as entanglement, involving particles at distant sites augmented by some classical communication. As with classical communication, one must be prepared to deal with noisy channels and much of this proposal deals with the mathematics of noisy channels. Some of this work has direct implications for experimental design, since it is important to know how to best allocate resources and choose coding schemes to minimize the effects of noise.

摘要该项目的主要重点是研究量子计算和信息理论中各种数学问题。 尽管构建量子计算机仍然是一个巨大的实验挑战，但它们有可能有效处理其计算复杂性使它们超出古典数字计算机范围的问题。 该提案的某些方面，例如误差校正和对多位门的探索，与量子计算直接相关。 但是，主要重点是量子通信相关领域的问题，尤其是通道容量，最佳编码和解码方案以及纠缠的分类。 P.I.过去在强磁场中对多粒子系统的分析，量子机械熵的特性以及操作员代数的地图的特性为开发解决这些挑战性问题所需的新数学工具提供了一个强大的起点。 使用量子计算机有效地考虑大量的可能性是对现有加密协议的安全性的潜在威胁。 幸运的是，使用量子粒子进行通信（实验上更可行）提供了分发加密密钥以及编码消息和传输信息的新机制。 这些程序包括基于用于编码和发送信息的量子粒子的传输；以及基于一种被称为纠缠的量子现象的创新新方案，涉及远处的颗粒，通过某些经典的交流增强。与古典交流一样，必须准备好处理嘈杂的渠道，大部分建议涉及嘈杂渠道的数学。 这项工作中的一些对实验设计具有直接影响，因为重要的是要知道如何最好地分配资源并选择编码方案以最大程度地减少噪声的影响。