CAREER: Applications of Quantum Information Theory

量子信息是研究量子力学作为一种信息理论意味着什么的学科。该理论引人注目但仍未完全被理解的特征包括测不准原理、纠缠、量子密码学和量子计算。拟议研究的第一部分将解决量子信息理论中的核心问题，这些问题一直是量子信息理论更广泛应用的障碍。例如：量子纠缠的“一夫一妻制”(或不可共享性)能在多大程度上区别于经典关联？一个系统中的信息包含在其短期或远程自由度中意味着什么？这项研究的第二部分将通过开发在凝聚态物理、优化算法和其他数学和物理领域的应用来扩大量子信息理论的覆盖范围。通过以上核心问题的研究进展，本研究希望开发更好的量子系统模拟，更好地理解纠缠如何在多体物理中发挥作用，并为困难的优化问题提供新的算法。预计这些工具不仅对量子信息的研究人员有用，而且对范围广泛的物理学家和计算机科学家也有用。这项研究将与一名研究生一起完成，研究生将从物理、计算机科学和数学中学习技术。此外，相关主题将融入本科教学。

Quantum information is the study of what quantum mechanics means as a theory of information. Striking, but still incompletely understood, features of the theory include the uncertainty principle, entanglement, quantum cryptography and quantum computing. The first part of the proposed research will tackle core questions in quantum information theory that have been barriers to its wider applicability. For example: to what extent can the "monogamy" (or non-shareability) of quantum entanglement be used to distinguish it from classical correlation? What does it mean for information in a system to be contained in its short-range or long-range degrees of freedom?The second part of this research will extend the reach of quantum information theory by developing applications in condensed-matter physics, optimization algorithms and other areas of math and physics. Through progress on the core problems above, this research hopes to develop better simulations of quantum systems, better understanding of how entanglement functions in many-body physics and new algorithms for hard optimization problems. These tools are expected to be of use not only to researchers in quantum information, but to a wide range of physicists and computer scientists. This research will be done together with a graduate student, who will learn techniques from physics, computer science and mathematics. Additionally, related topics will be integrated into undergraduate teaching.