Interactive Quantum Information Theory: Fundamentals and Applications

20世纪世纪科学的基石之一是克劳德·香农对信息论的发展。在一篇论文中，香农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，永远改变了我们接近压缩和纠错码的方式。这些定理构成了当前许多数字技术的基础，从移动的电话到文件压缩和互联网的通信层。传统上，通信是在单向设置中研究的，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，这些消息在数据通信速率上不是最佳的。通信复杂性是这种交互过程的数学理论，也是理论计算机科学中研究计算的核心模型之一。它在具体的计算模型中有多种实际应用，如流算法和数据结构。近年来，在经典的交互信息理论中出现了一系列的结果，将香农的结果扩展到了这种交互通信环境中。在过去的几十年里，这些想法的扩展已经在量子信息处理领域进行了研究，我们试图在亚原子水平上利用反直觉的自然规律，以便以与我们日常生活中经历的经典信息处理完全不同的方式处理信息。量子信息的独特性质使其本质上比经典信息更难处理，更容易受到噪音的影响。拟议研究计划的主要目标是为交互式量子通信协议开发信息理论，并将开发的工具应用于量子通信复杂性和其他具体量子计算模型中计算问题的复杂性研究。** 我提出的研究计划可以分为两个广泛的研究主题：香农压缩和纠错码的交互式量子类似物的发展。此外，我们开发了为这种交互式量子信息理论创建的工具的应用程序，以解决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。研究量子信息处理的主要原因之一是它导致了相对于经典信息处理的定性和定量优势，加拿大是开发这种量子技术的世界领导者。这是一个非常有前途的经济领域，我的计划也将有助于在这一领域形成有才华的科学家，这是加拿大新兴的经济部门，有许多年轻的有前途的公司。

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.