FET: Small: Frontiers of Quantum Shannon Theory

FET：小型：量子香农理论的前沿

• 批准号: 2329662
• 负责人: Mark Wilde
• 金额: $ 59.93万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-12-01 至 2026-11-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2329662&HistoricalAwards=false
• 关键词: FET; Small; Frontiers; Quantum; Shannon

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.

“量子香农理论前沿”奖的目标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在物理通信链路上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，它可以帮助实现比传统计算机更快的计算。实际上，物理通信链路会给通过它们传输的信息带来干扰，因此有必要执行校正程序来恢复该信息。这项研究对社会的好处是，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。分布式量子计算有潜力以比传统计算机更快的速度执行计算。同时，该奖项将涉及对几名研究生的培训，不仅在课堂上，而且在研究过程中，由研究者指导。更广泛地说，这位研究者是康奈尔量子日的主要组织者，这是一个三年一次的活动，康奈尔的学生、博士后和周围的研究社区聚集在一起，展示研究成果，参与科学讨论。在夏季，研究者还将高中生和本科生纳入他的研究小组，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，这个项目包括研究者要完成的几个任务。首先，研究者将研究一种被称为超激活效应的现象，在这种现象中，两个量子通信链路可以具有以非零速率发送量子信息的能力，即使这两个链路本身没有能力发送量子信息。具体地说，研究者将考虑在有限数量通道使用的非渐近状态下的这种现象。其次，研究者将通过量子态可接合性的概念研究任何物理链路上量子通信的局限性。这种可接合性概念在经典信息论中是没有意义的，但在量子信息论中由于纠缠现象而具有独特的意义。研究者还将研究计算给定量子态包含多少纠缠的方法，通过一种称为k-可扩展性的方法。具体来说，研究者将开发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，研究者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，因为这个概念更自然地与实验中产生的不理想状态相一致。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。