Interactive Quantum Information Theory: Fundamentals and Applications

交互式量子信息理论：基础与应用

• 批准号: RGPIN-2019-06197
• 负责人: Touchette, Dave
• 金额: $ 2.04万
• 依托单位: Université de Sherbrooke
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=757317
• 关键词: Interactive; Quantum; Information; Theory; Fundamentals

One of the cornerstones of 20th century science was the development of information theory by Claude Shannon. In a single paper, Shannon laid the mathematical foundations for a revolution in communication technology. His two quintessential results, the noiseless and noisy coding theorems, changed forever the way we approach compression and error correction codes. These theorems form the backbone for much of current digital technology, from mobile telephony to file compression and the communication layer of the Internet. Traditionally, communication is studied in a unidirectional setting, where a sender can wait for an arbitrarily long time to encode a long message; in contrast, with interactive communication, as in a conversation, it is necessary to transmit shorter messages that are not optimal in rate of data communication. Communication complexity is the mathematical theory of such interactive processes, and is one of the core models of computation studied in theoretical computer science. It has multiple practical applications to concrete models of computation such as streaming algorithms and data structures. Recent years have seen a flurry of results in classical interactive information theory, providing extensions of Shannon's results to this interactive communication setting. In the last decades, extensions of such ideas have been studied in the realm of quantum information processing, for which we try to harness the counter-intuitive laws of nature at the subatomic level in order to process information in fundamentally different ways than what is offered by classical information processing as experienced in our day-to-day lives. The unique properties of quantum information make it intrinsically harder to handle and more susceptible to noise than classical information. The main goal of the proposed research program is to develop a theory of information for interactive quantum communication protocols, and apply the developed tools to the study of the complexity of computational problems in quantum communication complexity and other concrete models of quantum computation. My proposed research program can be split into two broad research themes: the development of interactive quantum analogues to Shannon's compression and error correcting codes. Moreover, we develop applications of the tools created for such an interactive quantum information theory to relevant problems in quantum communication complexity and other concrete models of quantum computing. One of the main reasons to study quantum information processing is that it leads to qualitative and quantitative advantages over classical information processing, and Canada is a world leader in developing such quantum technology. This is a very promising economical area and my program will also serve towards the formation of talented scientists in this field which is a burgeoning economical sector in Canada, with many young promising companies.

克劳德·香农 (Claude Shannon) 的信息论发展是 20 世纪科学的基石之一，香农在一篇论文中为通信技术的革命奠定了数学基础，他的两个典型成果——无噪声和噪声编码定理——永远改变了信息论。这些定理构成了当前许多数字技术的支柱，从移动电话到文件压缩和互联网的通信层。传统上，通信是在单向环境中研究的。发送者可以等待任意长的时间来编码长消息；相反，在交互式通信中，如在对话中，有必要传输较短的消息，这在数据通信速率上不是最佳的。这种交互过程的理论，是理论计算机科学研究的核心计算模型之一，它在流算法和数据结构等具体计算模型中具有多种实际应用。信息论，提供香农理论的扩展在过去的几十年里，这种想法的扩展已经在量子信息处理领域得到了研究，为此我们试图利用亚原子层面的反直觉法则来处理信息。与我们日常生活中所经历的经典信息处理所提供的方式截然不同，量子信息的独特属性使其本质上比经典信息更难处理并且更容易受到噪声的影响。计划是开发交互式量子通信的信息理论我提出的研究计划可以分为两大研究主题：开发香农压缩的交互式量子模拟。此外，我们开发了为这种交互式量子信息理论创建的工具在量子通信复杂性和量子计算的其他具体模型中的相关问题的应用，这是研究量子信息处理的主要原因之一。与传统信息处理相比，具有定性和定量优势，加拿大是开发此类量子技术的世界领先者，这是一个非常有前途的经济领域，我的计划也将有助于培养该领域的才华横溢的科学家，这是加拿大蓬勃发展的经济部门，拥有许多年轻的有前途的公司。