CAREER: Applications of Quantum Information Theory

量子信息是研究量子力学作为信息理论的意义。该理论的特点引人注目，但仍未完全理解，包括不确定性原理，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，这些问题一直是其广泛应用的障碍。例如：量子纠缠的“一夫一妻制”（或不可共享性）在多大程度上可以用来区分它与经典相关？一个系统中的信息包含在它的短程或远程自由度中意味着什么？本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展量子信息理论的范围。通过在上述核心问题上的进展，本研究希望能够更好地模拟量子系统，更好地理解纠缠在多体物理中的作用，以及解决困难优化问题的新算法。预计这些工具不仅可以用于量子信息研究人员，还可以用于广泛的物理学家和计算机科学家。这项研究将与一名研究生一起完成，他将学习物理、计算机科学和数学方面的技术。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.