AF: CIF: Small: Theoretical Studies in Quantum Information and Computation

AF：CIF：小型：量子信息与计算的理论研究

• 批准号: 1017335
• 负责人: Yaoyun Shi
• 金额: $ 44.27万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-01 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1017335&HistoricalAwards=false
• 关键词: AF; CIF; Small; Theoretical; Studies

This project aims to deepen our understanding on two fundamental aspects of quantum information processing.(1) Entanglement manipulations and classifications. Quantum entanglement plays a central role in quantum information processing. An objective of the theory of quantum entanglement is to classify different types of entanglement according to their inter-convertibility through manipulations that do not require quantum communication. While bipartite entanglement is well understood in this framework, entanglement among three or more subsystems is inherently much more difficult. The PI is investigating properties of multipartite, especially tripartite, entanglement, with an emphasis of the algorithmic/computational complexity perspective. (2) Communication complexity. Communication complexity studies the inherent communication cost for distributed computing. This project addresses three important and related open problems: the Log-Rank Conjecture for characterizing the deterministic complexity; finding the largest possible gaps between the quantum and classical complexities; and the question if entanglement can dramatically reduce the cost for quantum communication. The plan to attack those difficult problems is to focus on some restricted classes of functions that are simple yet on which the problems remain open and challenging.

该项目旨在加深我们对量子信息处理的两个基本方面的理解。(1)纠缠处理和分类。 量子纠缠在量子信息处理中起着核心作用。 量子纠缠理论的一个目标是根据不同类型的纠缠通过不需要量子通信的操纵的相互转换性来分类。 虽然在这个框架中可以很好地理解两体纠缠，但三个或更多子系统之间的纠缠本质上要困难得多。 PI正在研究多体，特别是三方，纠缠的属性，重点是算法/计算复杂性的角度。(2)沟通的复杂性。 通信复杂性研究分布式计算的固有通信成本。 该项目解决了三个重要的相关开放问题：用于表征确定性复杂性的对数秩猜想;找到量子和经典复杂性之间的最大可能差距;以及纠缠是否可以显着降低量子通信成本的问题。 攻击这些困难问题的计划是集中在一些限制类的功能，是简单的，但对这些问题仍然开放和具有挑战性。