FET: Small: Frontiers of Quantum Shannon Theory

量子香农理论前沿奖的目的是在量子信息科学的几个领域进行理论研究。所有项目背后的主要思想是了解通过物理通信链路可以传输多少量子信息。量子信息是指对量子计算机处理和存储有用的信息，这些信息可以帮助实现比传统计算机更快的计算。实际上，物理通信链路会将干扰引入通过其传输的信息，因此需要执行纠正过程来恢复该信息。这项研究给社会带来的好处是，它将使人们更好地理解如何处理量子信息，这最终可能有利于分布式量子计算或秘密信息交换等任务。分布式量子计算有可能以比传统计算机更快的速度进行计算。同时，该奖项将涉及几名研究生的培训，不仅在课堂上，而且在研究过程中，由调查人员指导。更广泛地说，这位研究人员是康奈尔量子日的主要组织者，这是一个每三年举行一次的活动，康奈尔大学的学生和博士后以及周围的研究社区聚集在一起，展示研究成果，并参与科学讨论。在暑假期间，研究人员还会邀请高中生和本科生加入他的研究小组，学习基本的研究技能，并以量子信息协议和算法的编程和计算机模拟的形式为研究项目做出贡献。更详细地说，该项目包括几项由研究人员完成的任务。首先，研究人员将研究一种被称为超激活效应的现象，即两条量子通信链路可以以非零速率发送量子信息，即使这两条链路本身没有发送量子信息的能力。具体地说，调查者将在有限数量的信道使用的非渐近机制中考虑这一现象。其次，研究人员将通过一个称为量子态可接合性的概念来研究量子通信在任何物理链路上的局限性。这种可连接性的概念在经典信息论中没有意义，但由于纠缠现象，它在量子信息论中具有明显的意义。研究人员还将通过一种名为k-可扩充性的方法，研究计算给定量子态包含多少纠缠的方法。具体地说，研究人员将提出利用对称性和表示理论的算法，以显著减少基于k-可扩展性计算纠缠度量的运行时间。最后，研究人员将研究一个称为概率近似容量的通信容量概念，并获得这个量的界限，因为这个概念与实验中产生的不理想状态更自然地一致。这一奖项反映了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。

The goal of the award "Frontiers of Quantum Shannon Theory" is to pursue theoretical research in several domains of quantum information science. The main idea underlying all projects is to understand how much quantum information can be transmitted over a physical communication link. Quantum information refers to information that is useful for a quantum computer to process and store, and which can be helpful in realizing faster calculations than is possible with traditional computers. In reality, physical communication links introduce disturbances into the information that is transmitted over them, and it is necessary to perform correction procedures to recover that information. The benefit of this research to society is that it will lead to a greater understanding of how to process quantum information, which can ultimately be beneficial for tasks like distributed quantum computing or the exchange of secret information. Distributed quantum computation has the potential of performing calculations at a much faster pace than is possible with traditional computers. At the same time, the award will involve the training of several graduate students not only in the classroom but also in the research process, to be mentored by the investigator. More broadly, the investigator is a lead organizer of Cornell Quantum Day, a triannual event in which Cornell students and postdocs, and the surrounding research community, gather to present research results and engage in scientific discussions. During the summers, the investigator also takes on high school and undergraduate students into his research group to learn basic research skills and contribute to research projects in the form of programming and computer simulations of quantum information protocols and algorithms.In more detail, the project consists of several tasks to be pursued by the investigator. First, the investigator will research a phenomenon known as the superactivation effect, in which two quantum communication links can have an ability to send quantum information at a non-zero rate even if the two links have no ability to send quantum information on their own. Specifically, the investigator will consider this phenomenon in the non-asymptotic regime of a limited number of channel uses. Second, the investigator will research limitations of quantum communication over any physical link by means of a concept called joinability of quantum states. This concept of joinability is not meaningful in classical information theory, but it takes on a distinct meaning in quantum information theory due to the phenomenon of entanglement. The investigator will also research methods for calculating how much entanglement a given quantum state contains, by means of a method called k-extendibility. Specifically, the investigator will produce algorithms that exploit symmetry and representation theory to provide significant reductions in runtime for calculating measure of entanglement based on k-extendibility. Finally, the investigator will research a notion of communication capacity called probabilistic approximate capacity and obtain bounds on this quantity, as this concept aligns more naturally with the unideal states produced in experiments.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.